Results 51 to 60 of about 561,255 (240)
Difference Macdonald-Mehta Conjecture [PDF]
, 1997 In the paper we formulate and verify a difference counterpart of the Macdonald-Mehta conjecture and its generalization for the Macdonald polynomials.
Cherednik, Ivan
core +4 more sources
Factorization formulas for Macdonald polynomials
European Journal of Combinatorics, 2008 The aim of this note is to give some factorization formulas for different versions of the Macdonald polynomials when the parameter t is specialized at roots of unity, generalizing those existing for Hall-Littlewood functions.
Descouens, Francois, Morita, H.
openaire +4 more sources
Discrete Mathematics & Theoretical Computer Science, 2020 We conjecture two combinatorial interpretations for the symmetric function ∆eken, where ∆f is an eigenoperator for the modified Macdonald polynomials defined by Bergeron, Garsia, Haiman, and Tesler.
James Haglund +2 more
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An extension of MacMahon's Equidistribution Theorem to ordered multiset partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 A classical result of MacMahon states that inversion number and major index have the same distribution over permutations of a given multiset. In this work we prove a strengthening of this theorem originally conjectured by Haglund.
Andrew Timothy Wilson
doaj +1 more source
Macdonald polynomials in superspace: conjectural definition and positivity conjectures
, 2011 We introduce a conjectural construction for an extension to superspace of the Macdonald polynomials. The construction, which depends on certain orthogonality and triangularity relations, is tested for high degrees.
B. Feigin +19 more
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Yangian Gelfand-Zetlin Bases, gl(N)-Jack Polynomials and computation of Dynamical Correlation Functions in the Spin Calogero-Sutherland Model [PDF]
, 1997 We consider the gl(N)-invariant Calogero-Sutherland Models with N=1,2,3,... in a unified framework, which is the framework of Symmetric Polynomials.
Uglov, Denis
core +3 more sources
A combinatorial formula for Macdonald polynomials
Advances in Mathematics, 2011 In this paper we use the combinatorics of alcove walks to give a uniform combinatorial formula for Macdonald polynomials for all Lie types. These formulas are generalizations of the formulas of Haglund-Haiman-Loehr for Macdonald polynoimals of type GL(n).
Martha Yip, Arun Ram, Arun Ram
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Deformed Macdonald-Ruijsenaars Operators and Super Macdonald Polynomials [PDF]
Communications in Mathematical Physics, 2009 It is shown that the deformed Macdonald-Ruijsenaars operators can be described as the restrictions on certain affine subvarieties of the usual Macdonald-Ruijsenaars operator in infinite number of variables. The ideals of these varieties are shown to be generated by the Macdonald polynomials related to Young diagrams with special geometry.
Alexander P. Veselov +3 more
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Recursions and divisibility properties for combinatorial Macdonald polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Combinatorics
Nicholas A. Loehr, Elizabeth Niese
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Nonsymmetric Macdonald polynomials and matrix coefficients for unramified principal series [PDF]
, 2006 We show how a certain limit of the nonsymmetric Macdonald polynomials appears in the representation theory of semisimple groups over p--adic fields as matrix coefficients for the unramified principal series representations. The result is the nonsymmetric
Ion, Bogdan
core +2 more sources