منابع مشابه
On the quantum Kazhdan-Lusztig functor
One of the most exciting developments in representation theory in the recent years was the discovery of the Kazhdan-Lusztig functor [KL93a, KL93b, KL94a, KL94b], which is a tensor functor from the fusion category of representations of an affine Lie algebra to the category of representations of the corresponding quantum group, and is often an equivalence of categories. Informally speaking, this ...
متن کاملQuantum Schur Superalgebras and Kazhdan–lusztig Combinatorics
We introduce the notion of quantum Schur (or q-Schur) superalgebras. These algebras share certain nice properties with q-Schur algebras such as base change property, existence of canonical Z[v, v]-bases, and the duality relation with quantum matrix superalgebra A(m|n). We also construct a cellular Q(υ)-basis and determine its associated cells, called super-cells, in terms of a Robinson–Schenste...
متن کاملKazhdan-lusztig Cells
These are notes for a talk on Kazhdan-Lusztig Cells for Hecke Algebras. In this talk, we construct the Kazhdan-Lusztig basis for the Hecke algebra associated to an arbitrary Coxeter group, in full multiparameter generality. We then use this basis to construct a partition of the Coxeter group into the Kazhdan-Lusztig cells and describe the corresponding cell representations. Finally, we speciali...
متن کاملRelative Kazhdan–lusztig Cells
In this paper, we study the Kazhdan–Lusztig cells of a Coxeter group W in a “relative” setting, with respect to a parabolic subgroup WI ⊆ W . This relies on a factorization of the Kazhdan–Lusztig basis {Cw} of the corresponding (multi-parameter) Iwahori–Hecke algebra with respect to WI . We obtain two applications to the “asymptotic case” in type Bn, as introduced by Bonnafé and Iancu: we show ...
متن کاملImplementation of the Kazhdan–Lusztig algorithm
We denote D the set of parameters (of course the existence of the Cayley transform and cross action tables imply that the set D has already been enumerated, and thus identified with a set [0,M [ of integers.) We let M be the free A-module generated by D, where A = Z[v, v−1], and we write q = v2. We replace the canonical basis (Tδ)δ∈D of M by tδ = v Tδ, where l : D → N is the length function (al...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2002
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2002.v9.n4.a5