Algebras with Kazhdan-Lusztig theories
نویسنده
چکیده
منابع مشابه
Brundan-kazhdan-lusztig and Super Duality Conjectures
We formulate a general super duality conjecture on connections between parabolic categories O of modules over Lie superalgebras and Lie algebras of type A, based on a Fock space formalism of their Kazhdan-Lusztig theories which was initiated by Brundan. We show that the Brundan-Kazhdan-Lusztig (BKL) polynomials for gl(m|n) in our parabolic setup can be identified with the usual parabolic Kazhda...
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LET %’ be a highest weight category [CPSl] with finitely many simple objects and such that every object has finite length. Then Ce = mod S for a finite dimensional quasi-hereditary algebra S. In a series of papers, [CPS4,5,6,7], we have studied various Kazhdan-Lusztig theories for %. This concept arises naturally in, for example, the modular representation theory of semisimple algebraic groups....
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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...
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Let %‘A be the category of finite dimensional right modules for a quasi-hereditary algebra A. In the context of various types of Kazhdan-Lusztig theories, we study both the homological dual A! = Extt, (A/ rad(A), A/ rad(A)) and the graded algebra grA = @rad(A)j/rad(A)j+‘. For example, we investigate a condition introduced in [6], and here called (SKL’), which guarantees that A!’ E gr A. A stren...
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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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