Results 41 to 50 of about 18,306 (234)
Recurrence formulas for Macdonald polynomials of type A [PDF]
Journal of Algebraic Combinatorics, 2009 18 pages, LaTeX, revised version, to appear in Journal of Algebraic ...
Lassalle, Michel, Schlosser, Michael J.
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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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Canonical Basis and Macdonald Polynomials
Advances in Mathematics, 1998 In the basic representation of $U_q(\hat{sl}(2))$ realized via the algebra of symmetric functions we compare the canonical basis with the basis of Macdonald polynomials with $q=t^2$. We show that the Macdonald polynomials are invariant with respect to the bar involution defined abstractly on the representations of quantum groups. We also prove that the
Beck, Jonathan +2 more
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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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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 and Chromatic Quasisymmetric Functions [PDF]
The Electronic Journal of Combinatorics, 2020 We express the integral form Macdonald polynomials as a weighted sum of Shareshian and Wachs' chromatic quasisymmetric functions of certain graphs. Then we use known expansions of these chromatic quasisymmetric functions into Schur and power sum symmetric functions to provide Schur and power sum formulas for the integral form Macdonald polynomials ...
Haglund, James, Wilson, Andrew Timothy
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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 raising operator formula for Macdonald polynomials
Forum of Mathematics, SigmaWe give an explicit raising operator formula for the modified Macdonald polynomials $\tilde {H}_{\mu }(X;q,t)$ , which follows from our recent formula for $\nabla $ on an LLT polynomial and the Haglund-Haiman-Loehr formula expressing ...
J. Blasiak +4 more
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Some remarks on non-symmetric interpolation Macdonald polynomials
, 2019 We provide elementary identities relating the three known types of non-symmetric interpolation Macdonald polynomials. In addition we derive a duality for non-symmetric interpolation Macdonald polynomials.
Sahi, Siddhartha, Stokman, Jasper
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