Kazhdan-Lusztig-type multiplicity formula for symmetrizable generalized Kac-Moody algebras
نویسندگان
چکیده
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...
متن کاملKostka–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...
متن کاملA 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 ...
متن کاملA 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...
متن کاملOn a Diffeological Group Realization of Certain Generalized Symmetrizable Kac-Moody Lie Algebras
In this paper we utilize the notion of infinite dimensional diffeological Lie groups and diffeological Lie algebras to construct a Lie group structure on the space of smooth paths into a completion of a generalized Kac-Moody Lie algebra associated to a symmetrized generalized Cartan matrix. We then identify a large normal subgroup of this group of paths such that the quotient group has the soug...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1994
ISSN: 0386-2194
DOI: 10.3792/pjaa.70.94