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Nonsemisimple Macdonald polynomials [PDF]
Selecta Mathematica, 2009 The paper is mainly devoted to the irreducibility of the polynomial representation of the Double affine Hecke algebra, DAHA, for arbitrary reduced root systems and generic “central charge” q.
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Macdonald polynomials and cyclic sieving [PDF]
European Journal of Combinatorics, 2022 A new result added, 13 ...
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Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
Journal of High Energy Physics, 2017 We find new universal factorization identities for generalized Macdonald polynomials on the topological locus. We prove the identities (which include all previously known forumlas of this kind) using factorization identities for matrix model averages ...
Yegor Zenkevich
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On form factors and Macdonald polynomials [PDF]
Journal of High Energy Physics, 2013 We are developing the algebraic construction for form factors of local operators in the sinh-Gordon theory proposed in [B.Feigin, M.Lashkeivch, 2008]. We show that the operators corresponding to the null vectors in this construction are given by the degenerate Macdonald polynomials with rectangular partitions and the parameters $t=-q$ on the unit ...
Michael Lashkevich +3 more
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Hall-Littlewood Polynomials in terms of Yamanouchi words [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 This paper uses the theory of dual equivalence graphs to give explicit Schur expansions to several families of symmetric functions. We begin by giving a combinatorial definition of the modified Macdonald polynomials and modified Hall-Littlewood ...
Austin Roberts
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Rodrigues Formulas for the Macdonald Polynomials
Advances in Mathematics, 1997 We present formulas of Rodrigues type giving the Macdonald polynomials for arbitrary partitions through the repeated application of creation operators on the constant 1. Three expressions for the creation operators are derived one from the other.
Luc Lapointe, Luc Vinet
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The Classification of All Singular Nonsymmetric Macdonald Polynomials
Axioms, 2022 The affine Hecke algebra of type A has two parameters q,t and acts on polynomials in N variables. There are two important pairwise commuting sets of elements in the algebra: the Cherednik operators and the Jucys–Murphy elements whose simultaneous ...
Charles F. Dunkl
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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.
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Super-Macdonald polynomials: Orthogonality and Hilbert space interpretation [PDF]
Commun.Math.Phys. 388 (2021) 435-468, 2021 The super-Macdonald polynomials, introduced by Sergeev and Veselov, generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and they are eigenfunctions of the deformed Macdonald-Ruijsenaars operators introduced by the same authors.
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On Hamiltonians for Kerov functions
European Physical Journal C: Particles and Fields, 2020 Kerov Hamiltonians are defined as a set of commuting operators which have Kerov functions as common eigenfunctions. In the particular case of Macdonald polynomials, well known are the exponential Ruijsenaars Hamiltonians, but the exponential shape is not
A. Mironov, A. Morozov
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