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...
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We explain some remarkable connections between the twoparameter symmetric polynomials discovered in 1988 by Macdonald, and the geometry of certain algebraic varieties, notably the Hilbert scheme Hilb(C 2 ) of points in the plane, and the variety Cn of pairs of commuting n× n matrices.
متن کاملFactorisation of Macdonald polynomials
1. Macdonald polynomials Macdonald polynomials P λ (x; q, t) are orthogonal symmetric polynomials which are the natural multivariable generalisation of the continuous q-ultraspherical polyno-mials C n (x; β|q) [2] which, in their turn, constitute an important class of hyper-geometric orthogonal polynomials in one variable. Polynomials C n (x; β|q) can be obtained from the general Askey-Wilson p...
متن کاملMacdonald Polynomials and Algebraic Integrability
We construct explicitly (non-polynomial) eigenfunctions of the difference operators by Macdonald in case t = q, k ∈ Z. This leads to a new, more elementary proof of several Macdonald conjectures, first proved by Cherednik. We also establish the algebraic integrability of Macdonald operators at t = q (k ∈ Z), generalizing the result of Etingof and Styrkas. Our approach works uniformly for all ro...
متن کاملVector Valued Macdonald Polynomials
This paper defines and investigates nonsymmetric Macdonald polynomials with values in an irreducible module of the Hecke algebra of type AN−1. These polynomials appear as simultaneous eigenfunctions of Cherednik operators. Several objects and properties are analyzed, such as the canonical bilinear form which pairs polynomials with those arising from reciprocals of the original parameters, and t...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1998
ISSN: 0001-8708
DOI: 10.1006/aima.1998.1763