منابع مشابه
Kazhdan-lusztig Polynomials and Canonical Basis
In this paper we show that the Kazhdan–Lusztig polynomials (and, more generally, parabolic KL polynomials) for the group Sn coincide with the coefficients of the canonical basis in nth tensor power of the fundamental representation of the quantum group Uqslk. We also use known results about canonical bases for Uqsl2 to get a new proof of recurrent formulas for KL polynomials for maximal parabol...
متن کاملKazhdan–lusztig Cells and the Murphy Basis
Let H be the Iwahori–Hecke algebra associated with Sn, the symmetric group on n symbols. This algebra has two important bases: the Kazhdan–Lusztig basis and the Murphy basis. While the former admits a deep geometric interpretation, the latter leads to a purely combinatorial construction of the representations of H, including the Dipper–James theory of Specht modules. In this paper, we establish...
متن کاملA Factorization Theorem for Affine Kazhdan-lusztig Basis Elements
The lowest two-sided cell of the extended affine Weyl group We is the set {w ∈ We : w = x · w0 · z, for some x, z ∈ We}, denoted W(ν). We prove that for any w ∈ W(ν), the canonical basis element C w can be expressed as 1 [n]!χλ(Y )C ′ v1w0 C w0v2 , where χλ(Y ) is the character of the irreducible representation of highest weight λ in the Bernstein generators, and v1 and v −1 2 are what we call ...
متن کاملOn the Kazhdan-lusztig Basis of a Spherical Hecke Algebra
Lusztig proved that the Kazhdan-Lusztig basis of a spherical algebra can be essentially identified with the Weyl characters of the Langlands dual group. We generalize this result to the unequal parameter case. Our new proof is simple and quite different from Lusztig’s.
متن کاملLecture 10: Kazhdan-lusztig Basis and Categories O
In this and the next lecture we will describe an entirely different application of Hecke algebras, now to the category O. In the first section we will define the Kazhdan-Lusztig basis in the Hecke algebra of W and explain how to read the multiplicities in the category O from this basis (the Kazhdan-Lusztig conjecture proved independently by Beilinson-Bernstein and Brylinski-Kashiwara). In the r...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2012
ISSN: 1080-6377
DOI: 10.1353/ajm.2012.0031