Kazhdan-Lusztig-type multiplicity formula for symmetrizable generalized Kac-Moody algebras

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منابع مشابه

9 D ec 1 99 8 Kazhdan - Lusztig conjecture for symmetrizable Kac - Moody Lie algebras . III Positive

2 Highest weight modules 4 2.1 Kac-Moody Lie algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Integral Weyl groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Category of highest weight modules . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Enright functor for non-integral weights . . . . . . . . . . . . . . . . . . . . 11 2.5 Embeddings of Verma m...

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Kostka–foulkes Polynomials for Symmetrizable Kac–moody Algebras

We introduce a generalization of the classical Hall–Littlewood and Kostka–Foulkes polynomials to all symmetrizable Kac–Moody algebras. We prove that these Kostka–Foulkes polynomials coincide with the natural generalization of Lusztig’s t-analog of weight multiplicities, thereby extending a theorem of Kato. For g an affine Kac–Moody algebra, we define t-analogs of string functions and use Chered...

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A Half-twist Type Formula for the R-matrix of a Symmetrizable Kac-moody Algebra

Kirillov-Reshetikhin and Levendorskii-Soibelman developed a formula for the universal R-matrix of Uq(g) of the form R = (X ⊗X)∆(X). The action of X on a representation V permutes weight spaces according to the longest element in the Weyl group, so is only defined when g is of finite type. We give a similar formula which is valid for any symmetrizable KacMoody algebra. This is done by replacing ...

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A characterization of generalized Kac - Moody algebras

Generalized Kac-Moody algebras can be described in two ways: either using generators and relations, or as Lie algebras with an almost positive definite symmetric contravariant bilinear form. Unfortunately it is usually hard to check either of these conditions for any naturally occurring Lie algebra. In this paper we give a third characterization of generalized Kac-Moody algebras which is easier...

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On a Diffeological Group Realization of Certain Generalized Symmetrizable Kac-Moody Lie Algebras

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ژورنال

عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences

سال: 1994

ISSN: 0386-2194

DOI: 10.3792/pjaa.70.94