{VERSION 2 3 "IBM INTEL NT" "2.3" } {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 "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 20 "12-5-96,cry2tst2.mws" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 100 "This worksheet does some tensor prod uct calculations for A2=SU(3). It produces the crystal graphs of" }} {PARA 0 "" 0 "" {TEXT -1 24 "(a) the standard repn S," }}{PARA 0 "" 0 "" {TEXT -1 26 "(b) its contragredient S*," }}{PARA 0 "" 0 "" {TEXT -1 28 "(c) the tensor product SxS*," }}{PARA 0 "" 0 "" {TEXT -1 85 "(d ) the 8-dimensional subrepn of SxS* (i.e., the Cartan product of S, S* ), denoted T," }}{PARA 0 "" 0 "" {TEXT -1 27 "(e) the tensor product T xT." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "with(share);\nlibnam e:=libname,`c:\\\\MAPLEV4/share/algebra/crystal/cryhelp`;" }}{PARA 6 " " 1 "" {TEXT -1 70 "See ?share and ?share,contents for information abo ut the share library" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(libnameG6%%/C:\\MAPLEV4/libG%1C:\\MAPLEV4 /shareG%Ic:\\MAPLEV4/share/algebra/crystal/cryhelpG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "readshare(coxeter,algebra);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#%(coxeterG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "read(`c:/maplev4/share/algebra/crystal/crystal2.mpl`) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%Dtype~init_crystal();~to~initial ize.G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "init_crystal():" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#%5Crystal~initialized.G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "weyl[weights](A2);\nL1:=crystal[wei ght_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$F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "weyl[weyl _dim]((-1/3*e2-1/3*e1+2/3*e3),A2);\nL2:=crystal[weight_system](-(-1/3* e2-1/3*e1+2/3*e3),A2);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L2G7%7$\"\"!\"\"\"7$F(!\"\"7$F*F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(plots):\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "crystal[graphrep](L1,A2,G1); 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