@incollection {C98, AUTHOR = {Carter, R. W.}, TITLE = {Representations of simple {L}ie algebras: modern variations on a classical theme}, BOOKTITLE = {Algebraic groups and their representations (Cambridge, 1997)}, PAGES = {151--173}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {1998} } @article {C06, author = {Editorial Committee}, TITLE = {A note on the paper: ``{A} survey of the work of {G}eorge {L}usztig'' by {R}. {W}. {C}arter [{N}agoya {M}ath. {J}. {\bf 182} (2006), 1--45; \refcno 2235338]}, JOURNAL = {Nagoya Math. J.}, FJOURNAL = {Nagoya Mathematical Journal}, VOLUME = {183}, YEAR = {2006}, PAGES = {i--ii} } @Article{G01, author = {Graaf, W. A. de}, title = {Computing with quantized enveloping algebras: {PBW}-type bases, highest-weight modules, {$R$}-matrices}, journal = {J. Symbolic Comput.}, year = {2001}, volume = {32}, number = {5}, pages = {475--490} } @Article{G02, author = {Graaf, W. A. de}, title = {Constructing canonical bases of quantized enveloping algebras}, journal = {Experimental Mathematics}, year = {2002}, volume = {11}, number = {2}, pages = {161--170} } @book{H90, AUTHOR = {Humphreys, J. E.}, TITLE = {Reflection groups and {C}oxeter groups}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1990} } @Book{J96, author = {J. C. Jantzen}, title = {Lectures on Quantum Groups}, publisher = {American Mathematical Society}, year = {1996}, volume = {6}, series = {Graduate Studies in Mathematics} } @incollection {K96, AUTHOR = {Kashiwara, M.}, TITLE = {Similarity of crystal bases}, BOOKTITLE = {Lie algebras and their representations (Seoul, 1995)}, PAGES = {177--186}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1996} } @article {L90, AUTHOR = {G. Lusztig}, TITLE = {Quantum groups at roots of $1$}, JOURNAL = {Geom. Dedicata}, VOLUME = {35}, YEAR = {1990}, NUMBER = {1-3}, PAGES = {89--113} } @incollection {L92, AUTHOR = {Lusztig, G.}, TITLE = {Introduction to quantized enveloping algebras}, BOOKTITLE = {New developments in Lie theory and their applications (C\'ordoba, 1989)}, PAGES = {49--65}, PUBLISHER = {Birkh\"auser Boston}, ADDRESS = {Boston, MA}, YEAR = {1992} } @book {L93, AUTHOR = {G. Lusztig}, TITLE = {Introduction to quantum groups}, PUBLISHER = {Birkh\"auser Boston Inc.}, ADDRESS = {Boston, MA}, YEAR = {1993} } @article {L94, AUTHOR = {Littelmann, P.}, TITLE = {A {L}ittlewood-{R}ichardson rule for symmetrizable {K}ac-{M}oody algebras}, JOURNAL = {Invent. Math.}, VOLUME = {116}, YEAR = {1994}, NUMBER = {1-3}, PAGES = {329--346} } @article {L95, AUTHOR = {P. Littelmann}, TITLE = {Paths and root operators in representation theory}, JOURNAL = {Ann. of Math. (2)}, VOLUME = {142}, YEAR = {1995}, NUMBER = {3}, PAGES = {499--525} } @article {L96, AUTHOR = {G. Lusztig}, TITLE = {Braid group action and canonical bases}, JOURNAL = {Adv. Math.}, VOLUME = {122}, YEAR = {1996}, NUMBER = {2}, PAGES = {237--261} } @article {L98, AUTHOR = {Littelmann, P.}, TITLE = {Cones, crystals, and patterns}, JOURNAL = {Transform. Groups}, VOLUME = {3}, YEAR = {1998}, NUMBER = {2}, PAGES = {145--179} } @Manual{LN01, title = {GAPDoc, a GAP documentation meta-package}, author = {F. L\"{u}beck and M. Neunh\"{o}ffer}, year = {2001} } @article{R91, AUTHOR = {M. Rosso}, TITLE = {Repr\'esentations des groupes quantiques}, NOTE = {S\'eminaire Bourbaki, Vol.\ 1990/91}, JOURNAL = {Ast\'erisque}, FJOURNAL = {Ast\'erisque}, NUMBER = {201-203}, YEAR = {1991}, PAGES = {Exp.\ No.\ 744, 443--483 (1992)} } @incollection{S01, AUTHOR = {J. R. Stembridge}, TITLE = {Computational aspects of root systems, {C}oxeter groups, and {W}eyl characters}, BOOKTITLE = {Interaction of combinatorics and representation theory}, SERIES = {MSJ Mem.}, VOLUME = {11}, PAGES = {1--38}, PUBLISHER = {Math. Soc. Japan}, ADDRESS = {Tokyo}, YEAR = {2001} } @article {L0a, AUTHOR = {G. Lusztig}, TITLE = {Canonical bases arising from quantized enveloping algebras}, JOURNAL = {J. Amer. Math. Soc.}, VOLUME = {3}, YEAR = {1990a}, NUMBER = {2}, PAGES = {447--498} }