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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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A generalization of the Kostka-Foulkes polynomials [PDF]
, 1998 Combinatorial objects called rigged configurations give rise to q-analogues of certain Littlewood-Richardson coefficients. The Kostka-Foulkes polynomials and two-column Macdonald-Kostka polynomials occur as special cases.
Kirillov, Anatol N., Shimozono, Mark
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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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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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Baxter operator formalism for Macdonald polynomials [PDF]
, 2013 We develop basic constructions of the Baxter operator formalism for the Macdonald polynomials associated with root systems of type A. Precisely we construct a dual pair of mutually commuting Baxter operators such that the Macdonald polynomials are their ...
Anton Gerasimov +7 more
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Determinantal expressions for Macdonald polynomials
International Mathematics Research Notices, 1998 We show that the action of classical operators associated to the Macdonald polynomials on the basis of Schur functions, S_ [X(t-1)/(q-1)], can be reduced to addition in -rings. This provides explicit formulas for the Macdonald polynomials expanded in this basis as well as in the ordinary Schur basis, S_ [X], and the monomial basis, m_ [X].
Lapointe, L, Lascoux, Alain, Morse, J
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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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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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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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An analytic formula for Macdonald polynomials [PDF]
Comptes Rendus. Mathématique, 2003 8 pages; research announcement submitted to Comptes Rendus Math. Acad. Sci.
Lassalle, Michel, Schlosser, M.
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