This is TeX, Version 3.14159 (Web2C 7.3.1) (format=tex 2003.4.12) 4 FEB 2004 10:34 **flt (flt.tex (/usr/share/texmf/tex/amstex/base/amstex.tex AmS-TeX- Version 2.1 COPYRIGHT 1985, 1990, 1991 - AMERICAN MATHEMATICAL SOCIETY Use of this macro package is not restricted provided each use is acknowledged upon publication. Loading definitions for misc utility macros, page layout, accents/punctuation, line and page breaks, figures, comments, math spacing, fractions, smash commands, large operator symbols, integrals, operator names, multilevel sub/superscripts, matrices, multiline displays, continued fractions, compound symbols, various kinds of dots, special superscripts, \text, math font commands, \newsymbol, bold Greek and bold symbols, Euler fonts, math accents, roots, commutative diagrams, poor man's bold, syntax check, ... finished) (/usr/share/texmf/tex/amstex/base/amsppt.sty version 2.1h (1997/02/02): Loading utility definitions, more fonts, page dimension settings, top matter, section heads, theorems/proofs/definitions/remarks, rosters, footnotes, figures and captions, miscellaneous, references, end of document, output routine, \copyins=\insert252 hyphenation exceptions (U.S. English) (/usr/share/texmf/tex/amstex/config/amsppt.sti symbol names (/usr/share/texmf/tex/plain/amsfonts/amssym.tex) ,) ) [1] Underfull \vbox (badness 10000) has occurred while \output is active \vbox(544.7062+1.94444)x340.39218, glue set 10.67656 .\glue(\topskip) 3.05556 .\hbox(6.94444+1.94444)x340.39218, glue set - 0.03 ..\hbox(0.0+0.0)x20.0 ..\tenrm O ..\tenrm u ..\tenrm r ..\glue 3.33333 plus 1.66666 minus 1.11111 ..etc. .\penalty 150 .\glue(\baselineskip) 1.82222 .\hbox(8.23334+2.86108)x340.39218, glue set 0.61539 ..\tenrm r ..\tenrm e ..\tenrm p ..\tenrm r ..\tenrm e ..etc. .etc. [444] [445] Underfull \vbox (badness 1168) has occurred while \output is active \vbox(544.7062+1.94444)x340.39218, glue set 2.2727 .\glue(\topskip) 2.5 .\hbox(7.5+2.86108)x340.39218, glue set - 0.26234 ..\hbox(0.0+0.0)x20.0 ..\tenrm I ..\tenrm f ..\glue 3.33333 plus 1.66666 minus 1.11111 ..\mathon ..etc. .\penalty 150 .\glue(\lineskip) 1.0 .\hbox(8.23334+2.5)x340.39218, glue set - 0.15836 ..\teni ^^Z ..\glue(\thickmuskip) 2.77771 plus 2.77771 ..\tenrm : ..\penalty 500 ..\glue(\thickmuskip) 2.77771 plus 2.77771 ..etc. .etc. [446] Underfull \hbox (badness 10000) in paragraph at lines 312--314 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [447] Underfull \vbox (badness 10000) has occurred while \output is active \vbox(544.7062+2.5)x340.39218, glue set 5.47063 .\glue(\topskip) 2.5 .\hbox(7.5+2.5)x340.39218, glue set - 0.68105 ..\tenrm r ..\tenrm e ..\tenrm q ..\tenrm u ..\tenrm i ..etc. .\penalty 150 .\glue(\baselineskip) 2.0 .\hbox(7.5+2.5)x340.39218, glue set 0.5752 ..\teni E ..\kern0.57637 ..\mathoff ..\glue 3.33333 plus 1.66666 minus 1.11111 ..\tenrm h ..etc. .etc. [448] [449] Underfull \hbox (badness 10000) in paragraph at lines 439--441 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 Underfull \vbox (badness 10000) has occurred while \output is active \vbox(544.7062+0.0)x340.39218, glue set 10.2354 .\glue(\topskip) 3.05556 .\hbox(6.94444+1.94444)x340.39218, glue set 0.09677 ..\tenrm a ..\glue 3.33333 plus 1.66666 minus 1.11111 ..\tenrm n ..\tenrm e ..\tenrm w ..etc. .\penalty 150 .\glue(\baselineskip) 3.11111 .\hbox(6.94444+1.94444)x340.39218, glue set - 0.62932 ..\tenrm t ..\tenrm h ..\tenrm e ..\glue 3.33333 plus 1.66666 minus 1.11111 ..\tenrm s ..etc. .etc. [450] Underfull \hbox (badness 10000) in paragraph at lines 466--475 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 Underfull \vbox (badness 10000) has occurred while \output is active \vbox(544.7062+0.0)x340.39218, glue set 15.3531 .\glue(\topskip) 3.05556 .\hbox(6.94444+1.94444)x340.39218, glue set - 0.61394 ..\tenrm l ..\tenrm i ..\tenrm t ..\tenrm t ..\tenrm l ..etc. .\penalty 150 .\glue(\baselineskip) 3.11111 .\hbox(6.94444+1.94444)x340.39218, glue set - 0.84305 ..\tenrm t ..\tenrm h ..\tenrm e ..\glue 3.33333 plus 1.66666 minus 1.11111 ..\tenrm t ..etc. .etc. [451] Underfull \hbox (badness 10000) in paragraph at lines 502--510 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 Underfull \vbox (badness 10000) has occurred while \output is active \vbox(544.7062+0.0)x340.39218, glue set 10.2354 .\glue(\topskip) 3.05556 .\hbox(6.94444+1.94444)x340.39218, glue set 0.06473 ..\tenrm G ..\tenrm a ..\tenrm l ..\tenrm o ..\tenrm i ..etc. .\penalty 150 .\glue(\baselineskip) 2.55556 .\hbox(7.5+2.5)x340.39218, glue set 0.4386 ..\tenrm t ..\tenrm h ..\tenrm e ..\glue 3.33333 plus 1.66666 minus 1.11111 ..\tenrm w ..etc. .etc. [452] Underfull \hbox (badness 10000) in paragraph at lines 544--547 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 Underfull \vbox (badness 10000) has occurred while \output is active \vbox(544.7062+0.0)x340.39218, glue set 7.67656 .\glue(\topskip) 3.05556 .\hbox(6.94444+1.94444)x340.39218, glue set 0.58386 ..\tenrm c ..\tenrm o ..\tenrm m ..\tenrm m ..\tenrm o ..etc. .\penalty 150 .\glue(\baselineskip) 3.11111 .\hbox(6.94444+1.94444)x340.39218, glue set - 0.37473 ..\tenrm c ..\tenrm o ..\tenrm m ..\tenrm p ..\tenrm l ..etc. .etc. [453] Underfull \vbox (badness 10000) has occurred while \output is active \vbox(544.7062+0.0)x340.39218, glue set 5.66914 .\glue(\topskip) 3.05556 .\hbox(6.94444+1.94444)x340.39218, glue set - 0.51706 ..\tenrm i ..\tenrm n ..\kern-0.27779 ..\tenrm v ..\kern-0.55556 ..etc. .\penalty 150 .\glue(\baselineskip) 3.11111 .\hbox(6.94444+1.94444)x340.39218, glue set 0.40707 ..\tenrm J ..\tenrm u ..\tenrm n ..\tenrm e ..\tenrm , ..etc. .etc. [454] Underfull \vbox (badness 10000) has occurred while \output is active \vbox(544.7062+1.94444)x340.39218, glue set 5.55885 .\glue(\topskip) 3.05556 .\hbox(6.94444+1.94444)x340.39218, glue set 144.82817fil ..\glue 0.0 plus 1.0fil minus 1.0fil ..\tenbf C ..\tenbf h ..\tenbf a ..\tenbf p ..etc. .\glue(\parskip) 0.0 plus 1.0 .\glue(\baselineskip) 10.05556 .\hbox(0.0+0.0)x340.39218, glue set 320.39218fil ..\hbox(0.0+0.0)x20.0 ..\penalty 10000 ..\glue(\parfillskip) 0.0 plus 1.0fil ..\glue(\rightskip) 0.0 .etc. [455] Underfull \hbox (badness 3646) in paragraph at lines 676--680 []$ \tenrm tion as above, and that the de-for-ma-tion has a rep-re-sen-ta-tive \hbox(6.94444+1.94444)x340.39218, glue set 3.31732 .\hbox(0.0+0.0)x0.0 .\mathoff .\glue 24.0 .\tenrm t .\tenrm i .etc. [456] Underfull \hbox (badness 10000) in paragraph at lines 729--734 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [457] Underfull \hbox (badness 10000) in paragraph at lines 788--790 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [458] Underfull \hbox (badness 10000) in paragraph at lines 834--836 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [459] [460] Underfull \hbox (badness 10000) in paragraph at lines 912--922 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [461] Underfull \hbox (badness 10000) in paragraph at lines 959--965 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [462] Underfull \hbox (badness 10000) in paragraph at lines 1009--1012 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [463] [464] Underfull \hbox (badness 10000) in paragraph at lines 1099--1101 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [465] Underfull \hbox (badness 10000) in paragraph at lines 1122--1126 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 Underfull \hbox (badness 10000) in paragraph at lines 1132--1137 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 Underfull \hbox (badness 10000) in paragraph at lines 1140--1146 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [466] [467] Underfull \hbox (badness 10000) in paragraph at lines 1213--1221 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [468] Underfull \hbox (badness 10000) in paragraph at lines 1256--1260 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [469] Underfull \hbox (badness 10000) in paragraph at lines 1314--1316 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [470] Underfull \hbox (badness 1226) in paragraph at lines 1326--1329 []\tenrm We also give a char-ac-ter-i-za-tion of the or-thog-o-nal com-ple-ment s of \hbox(6.94444+1.94444)x340.39218, glue set 2.30946 .\hbox(0.0+0.0)x20.0 .\tenrm W .\kern-0.83334 .\tenrm e .\glue 3.33333 plus 1.66666 minus 1.11111 .etc. [471] [472] [473] Underfull \hbox (badness 10000) in paragraph at lines 1525--1529 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 Underfull \hbox (badness 10000) in paragraph at lines 1532--1536 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [474] [475] Underfull \vbox (badness 5147) has occurred while \output is active \vbox(544.7062+2.5)x340.39218, glue set 3.72356 .\glue(\topskip) 3.05556 .\hbox(6.94444+1.94444)x340.39218, glue set 0.09628 ..\hbox(0.0+0.0)x20.0 ..\tenit T ..\tenit h ..\tenit e ..\glue 3.57774 plus 1.53333 minus 1.0222 ..etc. .\penalty 400 .\glue(\baselineskip) 3.11111 .\hbox(6.94444+1.94444)x340.39218, glue set 145.01329fil ..\tenit s ..\discretionary replacing 2 ...\tenit o ...\tenit - ..\tenit o ..\kern-0.51112 ..\tenit c ..etc. .etc. [476] Underfull \hbox (badness 10000) in paragraph at lines 1682--1684 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [477] [478] Underfull \hbox (badness 10000) in paragraph at lines 1789--1792 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [479] Underfull \hbox (badness 10000) in paragraph at lines 1828--1831 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [480] Underfull \hbox (badness 10000) in paragraph at lines 1869--1874 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [481] Underfull \hbox (badness 10000) in paragraph at lines 1915--1919 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [482] Underfull \hbox (badness 10000) in paragraph at lines 1956--1961 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [483] Underfull \hbox (badness 2418) in paragraph at lines 1980--1983 \tenrm as a $\tenbf T$\tenrm -module. 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Also $[][][]\teni J[]\tenrm (\teni N\ tenrm )[] \tensy ' \tenbf T[]\tenrm (\teni N\tenrm )[]$ and \hbox(11.50008+6.50009)x340.39218, glue set 2.17569 .\tenrm s .\tenrm u .\tenrm l .\tenrm t .\glue 3.33333 plus 1.66666 minus 1.11111 .etc. Underfull \hbox (badness 10000) in paragraph at lines 2321--2323 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [492] [493] Underfull \hbox (badness 10000) in paragraph at lines 2412--2415 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [494] [495] [496] [497] Underfull \hbox (badness 10000) in paragraph at lines 2579--2583 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [498] [499] [500] [501] [502] Underfull \hbox (badness 10000) in paragraph at lines 2802--2809 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [503] Underfull \hbox (badness 10000) in paragraph at lines 2847--2849 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [504] Underfull \hbox (badness 1325) in paragraph at lines 2885--2890 \tenrm where the Eu-ler fac-tor of $\teni g$ \tenrm at $\teni q[]$ \tenrm (i.e. , of its as-so-ci-ated $\teni L$\tenrm -series) is \hbox(7.5+2.5)x340.39218, glue set 2.36847 .\tenrm w .\tenrm h .\tenrm e .\tenrm r .\tenrm e .etc. [505] Underfull \hbox (badness 10000) in paragraph at lines 2923--2926 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [506] Underfull \hbox (badness 10000) in paragraph at lines 2965--2967 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [507] [508] Underfull \hbox (badness 10000) in paragraph at lines 3029--3040 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [509] Underfull \hbox (badness 10000) in paragraph at lines 3084--3086 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [510] Underfull \vbox (badness 10000) has occurred while \output is active \vbox(544.7062+1.94444)x340.39218, glue set 6.86491 .\glue(\topskip) 2.5 .\hbox(7.5+2.5)x340.39218, glue set 0.14073 ..\tenrm t ..\kern-0.27779 ..\tenrm y ..\tenrm p ..\kern0.27779 ..etc. .\penalty 300 .\glue(\baselineskip) 2.55556 .\hbox(6.94444+1.94444)x340.39218, glue set 205.89197fil ..\tenrm t ..\tenrm h ..\tenrm e ..\glue 3.33333 plus 1.66666 minus 1.11111 ..\tenrm ^^M (ligature fl) ..etc. .etc. [511] Underfull \hbox (badness 10000) in paragraph at lines 3169--3172 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [512] [513] [514] Underfull \hbox (badness 10000) in paragraph at lines 3303--3304 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [515] [516] Underfull \vbox (badness 2073) has occurred while \output is active \vbox(544.7062+2.5)x340.39218, glue set 2.75027 .\glue(\topskip) 3.05556 .\hbox(6.94444+1.94444)x340.39218, glue set 144.82817fil ..\glue 0.0 plus 1.0fil minus 1.0fil ..\tenbf C ..\tenbf h ..\tenbf a ..\tenbf p ..etc. .\glue(\parskip) 0.0 plus 1.0 .\glue(\baselineskip) 10.05556 .\hbox(0.0+0.0)x340.39218, glue set 320.39218fil ..\hbox(0.0+0.0)x20.0 ..\penalty 10000 ..\glue(\parfillskip) 0.0 plus 1.0fil ..\glue(\rightskip) 0.0 .etc. [517] [518] Underfull \hbox (badness 10000) in paragraph at lines 3502--3504 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [519] [520] [521] Underfull \hbox (badness 10000) in paragraph at lines 3643--3645 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [522] Underfull \hbox (badness 10000) in paragraph at lines 3690--3696 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [523] Underfull \hbox (badness 10000) in paragraph at lines 3734--3738 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [524] [525] Underfull \hbox (badness 10000) in paragraph at lines 3832--3835 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [526] Underfull \hbox (badness 10000) in paragraph at lines 3878--3882 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [527] [528] Underfull \vbox (badness 1365) has occurred while \output is active \vbox(544.7062+0.0)x340.39218, glue set 2.39206 .\glue(\topskip) 1.85997 .\hbox(8.14003+2.75433)x340.39218, glue set - 0.67426 ..\hbox(0.0+0.0)x20.0 ..\tenrm O ..\tenrm u ..\tenrm r ..\glue 3.33333 plus 1.66666 minus 1.11111 ..etc. .\penalty 150 .\glue(\baselineskip) 1.10564 .\hbox(8.14003+2.75433)x340.39218, glue set - 0.63672 ..\tenrm t ..\tenrm i ..\tenrm m ..\tenrm a ..\tenrm t ..etc. .etc. [529] Underfull \hbox (badness 10000) in paragraph at lines 4002--4006 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [530] Underfull \hbox (badness 10000) in paragraph at lines 4045--4049 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [531] [532] Underfull \hbox (badness 10000) in paragraph at lines 4131--4136 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [533] Underfull \hbox (badness 10000) in paragraph at lines 4170--4174 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [534] Underfull \hbox (badness 10000) in paragraph at lines 4177--4181 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 Underfull \hbox (badness 2065) in paragraph at lines 4201--4214 \teni ^^T[]\tenrm (\teni ^^N\tenrm ) = \teni ^^T[]\tenrm (\teni ^^[[]^^N^^[\ten rm )$ for any $\teni ^^[$ \tenrm rep-re-sent-ing the non-triv-ial coset of \hbox(8.14003+2.86108)x340.39218, glue set 2.74603 .\teni ^^T .\hbox(4.51111+1.3611)x11.74623, shifted 1.49998 ..\sevenrm 0 ..\seveni ; ..\seveni ^^[ ..\kern0.25116 .\tenrm ( .\teni ^^N .\kern0.37846 .etc. Underfull \hbox (badness 10000) in paragraph at lines 4235--4238 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [535] [536] [537] Underfull \hbox (badness 10000) in paragraph at lines 4372--4374 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [538] Underfull \vbox (badness 1052) has occurred while \output is active \vbox(544.7062+0.0)x340.39218, glue set 2.1943 .\glue(\topskip) 2.5 .\hbox(7.5+2.5)x340.39218, glue set 0.47096 ..\tenrm t ..\tenrm o ..\glue 3.33333 plus 1.66666 minus 1.11111 ..\tenrm g ..\tenrm i ..etc. .\penalty 150 .\glue(\baselineskip) 2.0 .\hbox(7.5+4.30557)x340.39218, glue set - 0.57375 ..\tenbf T ..\hbox(4.51111+0.0)x4.48613, shifted 1.49998 ...\sevenrm 1 ..\tenrm ( ..\teni M ..\kern1.09026 ..etc. .etc. [539] [540] Underfull \hbox (badness 10000) in paragraph at lines 4524--4527 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [541] Underfull \hbox (badness 10000) in paragraph at lines 4563--4572 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 Underfull \vbox (badness 1158) has occurred while \output is active \vbox(544.7062+0.0)x340.39218, glue set 2.26285 .\glue(\topskip) 1.76666 .\hbox(8.23334+2.5)x340.39218, glue set 0.0133 ..\mathon ..\teni i ..\glue(\medmuskip) 2.22217 plus 1.11108 minus 2.22217 ..\tensy ^^N ..\penalty 700 ..etc. .\penalty 150 .\glue(\baselineskip) 2.55556 .\hbox(6.94444+1.94444)x340.39218, glue set 0.21455 ..\tenrm e ..\tenrm a ..\tenrm s ..\tenrm i ..\tenrm l ..etc. .etc. [542] Underfull \hbox (badness 10000) in paragraph at lines 4596--4614 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [543] [544] [545] Underfull \hbox (badness 10000) in paragraph at lines 4747--4749 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [546] Underfull \hbox (badness 10000) in paragraph at lines 4786--4792 \hbox(0.0+0.0)x340.39218 .\glue(\rightskip) 0.0 [547] [548] [549] [550] [551] ) Output written on flt.dvi (109 pages, 496804 bytes).