A Flag Whitney Number Formula for Matroid Kazhdan-Lusztig Polynomials
نویسندگان
چکیده
منابع مشابه
A Flag Whitney Number Formula for Matroid Kazhdan-Lusztig Polynomials
For a representation of a matroid the combinatorially defined Kazhdan-Lusztig polynomial computes the intersection cohomology of the associated reciprocal plane. However, these polynomials are difficult to compute and there are numerous open conjectures about their structure. For example, it is unknown whether or not the coefficients are non-negative for non-representable matroids. The main res...
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We associate to every matroid M a polynomial with integer coefficients, which we call the Kazhdan-Lusztig polynomial of M , in analogy with Kazhdan-Lusztig polynomials in representation theory. We conjecture that the coefficients are always non-negative, and we prove this conjecture for representable matroids by interpreting our polynomials as intersection cohomology Poincaré polynomials. We al...
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A nonrecursive scheme is presented to compute the KazhdanLusztig polynomials associated to a classical Hermitian symmetric space, extending a result of Lascoux-Schutzenberger for grassmannians. The polynomials for the exceptional Hermitian domains are also tabulated. All the KazhdanLusztig polynomials considered are shown to be monic.
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Motivated by a result of Fiebig (2007), we categorify some properties of Kazhdan-Lusztig polynomials via sheaves on Bruhat moment graphs. In order to do this, we develop new techniques and apply them to the combinatorial data encoded in these moment graphs. Résumé. Motivés par un resultat de Fiebig (2007), nous categorifions certaines propriétés des polynômes de KazhdanLusztig en utilisant fais...
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1. Lecture 1: Affine Lie algebras and the Fock representation of ĝln. 1.1. The loop algebra construction. Let g be a complex reductive Lie algebra and let L denote the algebra of Laurent polynomials in one variable L = C[t, t−1]. The loop algebra over g is L(g) = L ⊗ g, which is a Lie algebra with the bracket [t ⊗ x, t ⊗ y]0 = t[x, y]. (1.1) The elements of the loop algebra may be regarded as r...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/6120