A Statistical Study of the Kostka-Foulkes Polynomials
نویسندگان
چکیده
منابع مشابه
A Generalization of the Kostka-foulkes Polynomials
Combinatorial objects called rigged configurations give rise to q-analogues of certain Littlewood-Richardson coefficients. The Kostka-Foulkes polynomials and twocolumn Macdonald-Kostka polynomials occur as special cases. Conjecturally these polynomials coincide with the Poincaré polynomials of isotypic components of certain graded GL(n)-modules supported in a nilpotent conjugacy class closure i...
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plays an important role in the Garsia-Haglund proof of the q, t-Catalan conjecture, [2]. Let ΛQ(q,t) be the space of symmetric functions of degree n, over the field of rational functions Q(q, t), and let ∇ : ΛQ(q,t) → Λ n Q(q,t) be the Garsia-Bergeron operator. By studying recursions, Garsia and Haglund show that the coefficient of the elementary symmetric function en(X) in the image ∇(En,k(X))...
متن کاملSome Plethystic Identites and Kostka-foulkes Polynomials
plays an important role in the Garsia-Haglund proof of the q, t-Catalan conjecture, [2]. Let ΛQ(q,t) be the space of symmetric functions of degree n, over the field of rational functions Q(q, t), and let ∇ : ΛQ(q,t) → ΛQ(q,t) be the Garsia-Bergeron operator. By studying recursions, Garsia and Haglund show that the coefficient of the elementary symmetric function en(X) in the image∇(En,k(X)) of ...
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Generalized Hall–Littlewood polynomials (Macdonald spherical functions) and generalized Kostka–Foulkes polynomials (q-weight multiplicities) arise in many places in combinatorics, representation theory, geometry, and mathematical physics. This paper attempts to organize the different definitions of these objects and prove the fundamental combinatorial results from “scratch”, in a presentation w...
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A problem that arose in the study of the mass of the neutrino led us to the evaluation of a constant term with a variety of ramifications into several areas from Invariant Theory, Representation Theory, the Theory of Symmetric Functions and Combinatorics. A significant by-product of our evaluation is the construction of a trigraded Cohen Macaulay basis for the Invariants under an action of SL n...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1993
ISSN: 0196-8858
DOI: 10.1006/aama.1993.1014