{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "" -1 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 18 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 32 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 74 0 16 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 37 " \+ " }{TEXT 256 7 " " }{TEXT 257 7 "Crystal" }{TEXT 258 18 " test worksheet #2" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 261 "In this worksheet, we tensor the two fundamental re pns of A2 together. This tensor product is reducible and has an 8-dime nsional irreducible subrep.We both tensor this with itself and also re strict this 8-dim repn to A1. Both these crystal graphs are displayed. " }}{PARA 0 "" 0 "" {TEXT -1 20 "8-25-99,crytest2.mws" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "with(plo ts):\nwith(share);\nwith(coxeter);\nwith(weyl);" }}{PARA 6 "" 1 "" {TEXT -1 70 "See ?share and ?share,contents for information about the \+ share library" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7\"" }}{PARA 6 "" 1 " " {TEXT -1 23 "Share Library: coxeter" }}{PARA 6 "" 1 "" {TEXT -1 25 "Author: Stembridge, John." }}{PARA 6 "" 1 "" {TEXT -1 321 "Descriptio n: The coxeter package contains 30 basic procedures for studying root s systems and finite Coxeter groups. It can be used with The weyl pac kage which contains an additional seven procedures for manipulating we ight vectors and computing multiplicities for irreducible representati ons of semisimple Lie algebras." }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7@% %baseG%*char_polyG%*class_repG%+class_sizeG%+cox_matrixG%+cox_numberG% (degreesG%+descent_gfG%(diagramG%*exponentsG%-highest_rootG%,interior_ ptG%&iprodG%*length_gfG%,longest_eltG%)multpermG%(name_ofG%)num_reflG% &orbitG%+orbit_sizeG%*perm_charG%)perm_repG%*pos_rootsG%-presentationG %%rankG%'reduceG%(reflectG%,root_coordsG%%sizeG%'vec2fcG" }}{PARA 6 " " 1 "" {TEXT -1 20 "Share Library: weyl" }}{PARA 6 "" 1 "" {TEXT -1 25 "Author: Stembridge, John." }}{PARA 6 "" 1 "" {TEXT -1 217 "Descrip tion: The weyl package is a supplement to the coxeter package that co ntains 7 procedures for manipulating weight vectors and computing mult iplicities for irreducible representations of semisimple Lie algebras. " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7)%$rhoG%&storeG%.weight_coordsG%- weight_multsG%+weight_sysG%(weightsG%)weyl_dimG" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 44 "read(`e:/maplestuff/crystal/crystal26.mpl`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "in it_crystal():" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%5Crystal~initialized .G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "weyl[weights](A2);\nL 1:=crystal[weight_system](-(1/3*e2-2/3*e1+1/3*e3),A2);\n" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#7$,(%#e2G#\"\"\"\"\"$%#e1G#!\"#F(%#e3GF&,(F%#!\" \"F(F)F.F,#\"\"#F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L1G7%7$\"\"\" \"\"!7$!\"\"F'7$F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "weyl[weyl_dim]((-1/3*e2-1/ 3*e1+2/3*e3),A2);\nL2:=crystal[weight_system](-(-1/3*e2-1/3*e1+2/3*e3) ,A2);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L2G7%7$\"\"!\"\"\"7$F(!\"\"7$F*F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "#Note the difference in signs " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 56 "crystal[graphrep](L1,A2,G1);\ncrystal[showgraph](G1 ,1,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%.Graph~formed.G" }}{PARA 13 "" 1 "" {GLPLOT2D 385 385 385 {PLOTDATA 2 "6+-%'POINTSG6$7$\"\"\"\" \"!-%'SYMBOLG6#%'CIRCLEG-F$6$7$\"\"#F(F)-F$6$7$\"\"$F(F)-%'CURVESG6#7$ F&F/-F66#7$F/F3-%%TEXTG6%7$#F4F0F(Q\"16\"%+ALIGNABOVEG-F=6%7$#\"\"&F0F (Q\"2FBFC-%(SCALINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 0 2 9 1 1 1 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "crystal[graphrep](L2,A2,G2);\ncrystal[showgraph](G2,1 ,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%.Graph~formed.G" }}{PARA 13 " " 1 "" {GLPLOT2D 385 385 385 {PLOTDATA 2 "6+-%'POINTSG6$7$\"\"\"\"\"!- %'SYMBOLG6#%'CIRCLEG-F$6$7$\"\"#F(F)-F$6$7$\"\"$F(F)-%'CURVESG6#7$F&F/ -F66#7$F/F3-%%TEXTG6%7$#F4F0F(Q\"26\"%+ALIGNABOVEG-F=6%7$#\"\"&F0F(Q\" 1FBFC-%(SCALINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 0 2 9 1 1 1 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "crystal[graphprodrep](G1,G2,G3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%.Graph~formed.G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "Display the crystal graph of the tensor product of the two fundame ntal repns of A2." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "crysta l[showgraphprod](G3,1,3,1,3);" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6=-%'POINTSG6$7$\"\"\"F'-%'SYMBOLG6#%'CIRCLEG-F$6$7$ \"\"#F'F(-F$6$7$\"\"$F'F(-F$6$7$F'F/F(-F$6$7$F/F/F(-F$6$7$F3F/F(-F$6$7 $F'F3F(-F$6$7$F/F3F(-F$6$7$F3F3F(-%'CURVESG6#7$F&F6-FG6#7$F6F?-FG6#7$F &F.-FG6#7$F?FB-FG6#7$F.F9-FG6#7$F9F<-FG6#7$FBFE-FG6#7$F " 0 "" {MPLTEXT 1 0 43 "crystal[linsubgraphrep]( 2*e1+e2,A2,G3,G4);\n" }{TEXT -1 32 "8-dimensional irreducible subrep" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%.Graph~formed.G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "crystal[branch]([2],G4,G5);\ncrystal[showgr aph](G5,1,8);\n" }{TEXT -1 30 "restrict this 8-dim repn to A1" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%5Branch~graph~formed.G" }}{PARA 13 " " 1 "" {GLPLOT2D 385 385 385 {PLOTDATA 2 "64-%'POINTSG6$7$\"\"\"\"\"!- %'SYMBOLG6#%'CIRCLEG-F$6$7$\"\"#F(F)-F$6$7$\"\"$F(F)-F$6$7$\"\"%F(F)-F $6$7$\"\"&F(F)-F$6$7$\"\"'F(F)-F$6$7$\"\"(F(F)-F$6$7$\"\")F(F)-%'CURVE SG6#7&F&7$F0#F'F0FMF3-FJ6#7&F/7$F4FNFRF7-FJ6#7&F77$F \+ " 0 "" {MPLTEXT 1 0 27 "crystal[showgraph](G4,1,8);" }}{PARA 13 "" 1 " " {GLPLOT2D 385 385 385 {PLOTDATA 2 "6<-%'POINTSG6$7$\"\"\"\"\"!-%'SYM BOLG6#%'CIRCLEG-F$6$7$\"\"#F(F)-F$6$7$\"\"$F(F)-F$6$7$\"\"%F(F)-F$6$7$ \"\"&F(F)-F$6$7$\"\"'F(F)-F$6$7$\"\"(F(F)-F$6$7$\"\")F(F)-%'CURVESG6#7 $F&F/-FJ6#7&F&7$F0#F'F0FPF3-FJ6#7&F/7$F4FQFUF7-FJ6#7&F37$F8FQFYF;-FJ6# 7&F77$F " 0 "" {MPLTEXT 1 0 32 "crystal[graphprodrep](G4,G4,G6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%.Graph~formed.G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "crystal[showgraphprod](G6,1,8,1,8);" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6fx-%'POINTSG6$7$\"\"\"F'-%'SYMBOLG 6#%'CIRCLEG-F$6$7$\"\"#F'F(-F$6$7$\"\"$F'F(-F$6$7$\"\"%F'F(-F$6$7$\"\" &F'F(-F$6$7$\"\"'F'F(-F$6$7$\"\"(F'F(-F$6$7$\"\")F'F(-F$6$7$F'F/F(-F$6 $7$F/F/F(-F$6$7$F3F/F(-F$6$7$F7F/F(-F$6$7$F;F/F(-F$6$7$F?F/F(-F$6$7$FC F/F(-F$6$7$FGF/F(-F$6$7$F'F3F(-F$6$7$F/F3F(-F$6$7$F3F3F(-F$6$7$F7F3F(- F$6$7$F;F3F(-F$6$7$F?F3F(-F$6$7$FCF3F(-F$6$7$FGF3F(-F$6$7$F'F7F(-F$6$7 $F/F7F(-F$6$7$F3F7F(-F$6$7$F7F7F(-F$6$7$F;F7F(-F$6$7$F?F7F(-F$6$7$FCF7 F(-F$6$7$FGF7F(-F$6$7$F'F;F(-F$6$7$F/F;F(-F$6$7$F3F;F(-F$6$7$F7F;F(-F$ 6$7$F;F;F(-F$6$7$F?F;F(-F$6$7$FCF;F(-F$6$7$FGF;F(-F$6$7$F'F?F(-F$6$7$F /F?F(-F$6$7$F3F?F(-F$6$7$F7F?F(-F$6$7$F;F?F(-F$6$7$F?F?F(-F$6$7$FCF?F( -F$6$7$FGF?F(-F$6$7$F'FCF(-F$6$7$F/FCF(-F$6$7$F3FCF(-F$6$7$F7FCF(-F$6$ 7$F;FCF(-F$6$7$F?FCF(-F$6$7$FCFCF(-F$6$7$FGFCF(-F$6$7$F'FGF(-F$6$7$F/F GF(-F$6$7$F3FGF(-F$6$7$F7FGF(-F$6$7$F;FGF(-F$6$7$F?FGF(-F$6$7$FCFGF(-F $6$7$FGFGF(-%'CURVESG6#7$F&FJ-F[x6#7&F&7$#F'F/F/FaxF\\o-F[x6#7&FJ7$Fbx F3FfxFdp-F[x6#7&F\\o7$FbxF7FjxF\\r-F[x6#7&Fdp7$FbxF;F^yFds-F[x6#7&F\\r 7$FbxF?FbyF\\u-F[x6#7&Fds7$FbxFCFfyFdv-F[x6#7$F\\uFdv-F[x6#7$FJFM-F[x6 #7$FdpFgp-F[x6#7$F\\uF_u-F[x6#7$FdvFgv-F[x6#7&F\\o7$F/#FCF/FizFbo-F[x6 #7&F\\r7$F/#\"#6F/F^[lFbr-F[x6#7&Fds7$F/#\"#8F/Fd[lFjs-F[x6#7&Fdv7$F/# \"#-F[x6#7&Feo7$F;FjzFcblF[p -F[x6#7&F]q7$F;F]`lFgblFcq-F[x6#7&Fer7$F;F_[lF[clF[s-F[x6#7&F]t7$F;Fe[ lF_clFct-F[x6#7&Feu7$F;Fc`lFcclF[v-F[x6#7&F]w7$F;F[\\lFgclFcw-F[x6#7&F :7$F]`lF/F[dlFho-F[x6#7&FV7$F]`lF3F_dlF`q-F[x6#7&Fho7$F]`lF7FcdlFhr-F[ x6#7&F`q7$F]`lF;FgdlF`t-F[x6#7$FhuF`w-F[x6#7&F:7$F?Fa\\lF^elFB-F[x6#7& FV7$F?Fh^lFbelFfn-F[x6#7&F`q7$F?F]`lFfelFfq-F[x6#7&Fhr7$F?F_[lFjelF^s- F[x6#7&F`t7$F?Fe[lF^flFft-F[x6#7&Fhu7$F?Fc`lFbflF^v-F[x6#7&F`w7$F?F[\\ lFfflFfw-F[x6#7$F>FY-F[x6#7&F[p7$F_[lF7F]glF[s-F[x6#7&F[s7$F_[lF?FaglF [v-F[x6#7&Fct7$F_[lFCFeglFcw-F[x6#7&FY7$FCFh^lFiglFin-F[x6#7&Fcq7$FCF] `lF]hlFiq-F[x6#7&F[v7$FCFc`lFahlFav-F[x6#7&Fcw7$FCF[\\lFehlFiw-F[x6#7& FB7$Fe[lF/FihlF^p-F[x6#7&Ffn7$Fe[lF3F]ilFfq-F[x6#7&Ffq7$Fe[lF;FailFft- F[x6#7$F^vFfw-F[x6#7$F^pFap-F[x6#7$F^sFas-F[x6#7$FftFit-F[x6#7$FfwFiw- F[x6#7&Fin7$Fc`lF3FdjlFiq-F[x6#7&Fap7$Fc`lF7FhjlFas-%%TEXTG6%7$F'Fa\\l Q\"26\"%*ALIGNLEFTG-Fjjl6%FaxQ\"1F^[mF_[m-Fjjl6%FfxFb[mF_[m-Fjjl6%FjxF ][mF_[m-Fjjl6%F^yFb[mF_[m-Fjjl6%FbyF][mF_[m-Fjjl6%FfyF][mF_[m-Fjjl6%7$ F'Fc`lFb[mF_[m-Fjjl6%F`\\lF][m%+ALIGNABOVEG-Fjjl6%Fi\\lF][mFb\\m-Fjjl6 %7$Fa\\lFCF][mFb\\m-Fjjl6%7$Fa\\lFGF][mFb\\m-Fjjl6%FizFb[mFb\\m-Fjjl6% F^[lFb[mFb\\m-Fjjl6%Fd[lFb[mFb\\m-Fjjl6%Fj[lFb[mFb\\m-Fjjl6%F`\\lFb[mF _[m-Fjjl6%Fe\\lFb[mF_[m-Fjjl6%Fi\\lF][mF_[m-Fjjl6%F]]lFb[mF_[m-Fjjl6%7 $F/Fc`lFb[mF_[m-Fjjl6%Fd]lFb[mFb\\m-Fjjl6%Fh]lFb[mFb\\m-Fjjl6%F\\^lFb[ mFb\\m-Fjjl6%F`^lFb[mFb\\m-Fjjl6%7$F3Fa\\lF][mF_[m-Fjjl6%Fg^lFb[mF_[m- Fjjl6%F\\_lF][mF_[m-Fjjl6%F`_lF][mF_[m-Fjjl6%Fd_lF][mF_[m-Fjjl6%Fh_lF] [mFb\\m-Fjjl6%F\\`lF][mFb\\m-Fjjl6%Fb`lF][mFb\\m-Fjjl6%Fh`lF][mFb\\m-F jjl6%7$F7Fa\\lF][mF_[m-Fjjl6%F_alFb[mF_[m-Fjjl6%FcalF][mF_[m-Fjjl6%Fga lF][mF_[m-Fjjl6%F[blF][mF_[m-Fjjl6%F_blFb[mFb\\m-Fjjl6%FcblFb[mFb\\m-F jjl6%FgblFb[mFb\\m-Fjjl6%F[clFb[mFb\\m-Fjjl6%F_clFb[mFb\\m-Fjjl6%FcclF b[mFb\\m-Fjjl6%FgclFb[mFb\\m-Fjjl6%F[dlFb[mF_[m-Fjjl6%F_dlFb[mF_[m-Fjj l6%FcdlF][mF_[m-Fjjl6%FgdlFb[mF_[m-Fjjl6%FcclFb[mF_[m-Fjjl6%F^elF][mFb \\m-Fjjl6%FbelF][mFb\\m-Fjjl6%FfelF][mFb\\m-Fjjl6%FjelF][mFb\\m-Fjjl6% F^flF][mFb\\m-Fjjl6%FbflF][mFb\\m-Fjjl6%FfflF][mFb\\m-Fjjl6%F^elF][mF_ [m-Fjjl6%F]glF][mF_[m-Fjjl6%FaglF][mF_[m-Fjjl6%FeglF][mF_[m-Fjjl6%Figl F][mFb\\m-Fjjl6%F]hlF][mFb\\m-Fjjl6%FahlF][mFb\\m-Fjjl6%FehlF][mFb\\m- Fjjl6%FihlFb[mF_[m-Fjjl6%F]ilFb[mF_[m-Fjjl6%FailFb[mF_[m-Fjjl6%FahlFb[ mF_[m-Fjjl6%FdjlFb[mFb\\m-Fjjl6%7$Fc`lF;Fb[mFb\\m-Fjjl6%7$Fc`lF?Fb[mFb \\m-Fjjl6%7$Fc`lFGFb[mFb\\m-Fjjl6%FdjlFb[mF_[m-Fjjl6%FhjlF][mF_[m-%(SC ALINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 0 2 9 1 1 1 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "3 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }