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[2] (./hecke.toc
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Chapter 1.
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Chapter 2.
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Chapter 3.
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[]\T1/ptm/m/n/10.95 The hi-er-ar-chy of mod-ule ob-jects is more com-plex. On t
op we have the fil-ter
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\T1/ptm/m/n/10.95 o-gously, \T1/cmtt/m/n/10.95 IsSchurModule \T1/ptm/m/n/10.95 
is su-per-fil-ter of \T1/cmtt/m/n/10.95 IsSchurWeyl\T1/ptm/m/n/10.95 , \T1/cmtt
/m/n/10.95 IsSchurPIM\T1/ptm/m/n/10.95 , \T1/cmtt/m/n/10.95 IsSchurSimple \T1/p
tm/m/n/10.95 and
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\T1/cmtt/m/n/10.95 IsFockSchurModule \T1/ptm/m/n/10.95 which it-self is su-per-
fil-ter of \T1/cmtt/m/n/10.95 IsFockSchurWeyl\T1/ptm/m/n/10.95 , \T1/cmtt/m/n/1
0.95 IsFockSchurPIM\T1/ptm/m/n/10.95 ,
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\T1/cmtt/m/n/10.95 IsFockSchurSimple\T1/ptm/m/n/10.95 . Fur-ther, there are sub
-fil-ter re-la-tions be-tween \T1/cmtt/m/n/10.95 IsFockSpecht \T1/ptm/m/n/10.95
 and
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\T1/cmtt/m/n/10.95 IsHeckeSpecht \T1/ptm/m/n/10.95 etc., \T1/cmtt/m/n/10.95 IsF
ockSchurWeyl \T1/ptm/m/n/10.95 and \T1/cmtt/m/n/10.95 IsFockSpecht \T1/ptm/m/n/
10.95 etc., \T1/cmtt/m/n/10.95 IsFockSchurWeyl \T1/ptm/m/n/10.95 and
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[]\T1/ptm/m/n/10.95 For de-com-po-si-tion ma-tri-ces we use the fil-ter \T1/cmt
t/m/n/10.95 IsDecompositionMatrix \T1/ptm/m/n/10.95 and its sub-fil-ter
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[14]
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[]\T1/ptm/m/n/10.95 Notice that, un-like \T1/cmtt/m/n/10.95 MakePIM \T1/ptm/m/n
/10.95 ([][]3.2.3[][]) and \T1/cmtt/m/n/10.95 MakeSpecht \T1/ptm/m/n/10.95 ([][
]3.2.3[][]), the only ar-gu-ments which
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[15]
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[]\T1/ptm/m/n/10.95 See also \T1/cmtt/m/n/10.95 Specht \T1/ptm/m/n/10.95 ([][]3
.2.1[][]). This func-tion re-quires the pack-age \T1/phv/m/n/10.95 hecke \T1/pt
m/m/n/10.95 (see \T1/cmtt/m/n/10.95 LoadPackage
 []


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[]\T1/cmtt/m/n/10.95 DecompositionMatrix \T1/ptm/m/n/10.95 first checks whether
 the re-quired de-com-po-si-tion ma-trix ex-ists as
 []


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\T1/ptm/m/n/10.95 a li-brary file (check-ing first in the cur-rent di-rec-tory,
 next in the di-rec-tory spec-i-fied by
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[16]
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[]\T1/ptm/m/n/10.95 By de-fault, the rows and columns of the de-com-po-si-tion 
ma-tri-ces are or-dered
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\T1/ptm/m/n/10.95 ma-tri-ces into \T1/phv/m/n/10.95 GAP \T1/ptm/m/n/10.95 ma-tr
i-ces and vice versa (see \T1/cmtt/m/n/10.95 MatrixDecompositionMatrix \T1/ptm/
m/n/10.95 ([][]3.5.7[][]) and
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\T1/phv/m/n/10.95 Hecke \T1/ptm/m/n/10.95 pro-vides four func-tions \T1/cmtt/m/
n/10.95 RInducedModule \T1/ptm/m/n/10.95 ([][]3.4.1[][]), \T1/cmtt/m/n/10.95 RR
estrictedModule \T1/ptm/m/n/10.95 ([][]3.4.3[][]),
 []


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\T1/cmtt/m/n/10.95 SInducedModule \T1/ptm/m/n/10.95 ([][]3.4.2[][]) and \T1/cmt
t/m/n/10.95 SRestrictedModule \T1/ptm/m/n/10.95 ([][]3.4.4[][]) for in-duc-ing 
and re-strict-ing mod-
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[21]
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[]\T1/ptm/m/n/10.95 When more than one residue if given to \T1/cmtt/m/n/10.95 R
RestrictedModule
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\T1/ptm/m/n/10.95 it re-turns \T1/cmtt/m/n/10.95 RRestrictedModule($\OML/ztmcm/
m/it/10.95 x; r[]; r[]; [] ; r[]$\T1/cmtt/m/n/10.95 )\T1/ptm/m/n/10.95 = \T1/cm
tt/m/n/10.95 RRestrictedModule(
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[]\T1/ptm/m/n/10.95 As with \T1/cmtt/m/n/10.95 RInducedModule \T1/ptm/m/n/10.95
 ([][]3.4.1[][]), when \T1/cmtt/m/n/10.95 RRestrictedModule \T1/ptm/m/n/10.95 i
s ap-plied to the canon-i-
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[22]
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[]\T1/ptm/m/n/10.95 Almost all of the de-com-po-si-tion ma-tri-ces in-cluded in
 \T1/phv/m/n/10.95 Hecke \T1/ptm/m/n/10.95 were cal-cu-lated di-rectly
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\T1/ptm/m/n/10.95 by \T1/cmtt/m/n/10.95 InducedDecompositionMatrix\T1/ptm/m/n/1
0.95 . When $\OML/ztmcm/m/it/10.95 n$ \T1/ptm/m/n/10.95 is ``small'' \T1/cmtt/m
/n/10.95 InducedDecompositionMatrix \T1/ptm/m/n/10.95 is
 []


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\T1/ptm/m/n/10.95 usu-ally able to re-turn the full de-com-po-si-tion ma-trix f
or $\OML/ztmcm/m/it/10.95 H\OT1/ztmcm/m/n/10.95 (\OML/ztmcm/m/it/10.95 S[]\OT1/
ztmcm/m/n/10.95 )$\T1/ptm/m/n/10.95 . Fi-nally, al-though the
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[]\T1/cmtt/m/n/10.95 IsNewIndecomposable \T1/ptm/m/n/10.95 is the func-tion whi
ch does all of the hard work when the
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\T1/ptm/m/n/10.95 func-tion \T1/cmtt/m/n/10.95 InducedDecompositionMatrix \T1/p
tm/m/n/10.95 ([][]3.5.1[][]) is ap-plied to de-com-po-si-tion ma-tri-ces.
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\T1/phv/m/n/10.95 Hecke \T1/ptm/m/n/10.95 has two func-tions for cal-cu-lat-ing
 the di-men-sions of mod-ules of Hecke al-ge-bras;
 []


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\T1/ptm/m/n/10.95 See also \T1/cmtt/m/n/10.95 GoodNodes \T1/ptm/m/n/10.95 ([][]
3.7.6[][]). This func-tion re-quires the pack-age \T1/phv/m/n/10.95 hecke \T1/p
tm/m/n/10.95 (see \T1/cmtt/m/n/10.95 LoadPackage
 []


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[34]
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\T1/ptm/m/n/10.95 See also \T1/cmtt/m/n/10.95 GoodNodes \T1/ptm/m/n/10.95 ([][]
3.7.6[][]). This func-tion re-quires the pack-age \T1/phv/m/n/10.95 hecke \T1/p
tm/m/n/10.95 (see \T1/cmtt/m/n/10.95 LoadPackage
 []


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[]\T1/ptm/m/n/10.95 The $\OML/ztmcm/m/it/10.95 e$\T1/ptm/m/n/10.95 -residue of 
the $\OT1/ztmcm/m/n/10.95 (\OML/ztmcm/m/it/10.95 i; j\OT1/ztmcm/m/n/10.95 )$\T1
/ptm/m/n/10.95 -th node in the di-a-gram of a par-ti-tion $\OML/ztmcm/m/it/10.9
5 ^^V$ \T1/ptm/m/n/10.95 is $\OT1/ztmcm/m/n/10.95 (\OML/ztmcm/m/it/10.95 j \OMS
/ztmcm/m/n/10.95 ^^@ \OML/ztmcm/m/it/10.95 i\OT1/ztmcm/m/n/10.95 )  []  \OML/zt
mcm/m/it/10.95 e$\T1/ptm/m/n/10.95 .
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[]\T1/ptm/b/n/10.95 Returns:  \T1/ptm/m/n/10.95 the list of $\OML/ztmcm/m/it/10
.95 e$\T1/ptm/m/n/10.95 -regular par-ti-tions of $\OML/ztmcm/m/it/10.95 n$\T1/p
tm/m/n/10.95 , or-dered re-verse lex-i-co-graph-i-cally (see
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\T1/ptm/m/n/10.95 in \T1/cmtt/m/n/10.95 CrystalDecompositionMatrix \T1/ptm/m/n/
10.95 ([][]3.2.9[][]). This func-tion re-quires the pack-age \T1/phv/m/n/10.95 
hecke \T1/ptm/m/n/10.95 (see
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\T1/ptm/m/n/10.95 See also \T1/cmtt/m/n/10.95 SemiStandardTableaux \T1/ptm/m/n/
10.95 ([][]3.10.2[][]). This func-tion re-quires the pack-age \T1/phv/m/n/10.95
 hecke \T1/ptm/m/n/10.95 (see
 []

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