Results 31 to 40 of about 18,306 (234)
(q,t)-deformed (skew) Hurwitz τ-functions
Nuclear Physics B, 2023 We follow the general recipe for constructing commutative families of W-operators, which provides Hurwitz-like expansions in symmetric functions (Macdonald polynomials), in order to obtain a difference operator example that gives rise to a (q,t ...
Fan Liu +6 more
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Can tangle calculus be applicable to hyperpolynomials?
Nuclear Physics B, 2019 We make a new attempt at the recently suggested program to express knot polynomials through topological vertices, which can be considered as a possible approach to the tangle calculus: we discuss the Macdonald deformation of the relation between the ...
Hidetoshi Awata +3 more
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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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Matrix product formula for Macdonald polynomials [PDF]
, 2015 We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik--Zamolodchikov equations, which arise by considering representations of the Zamolodchikov--Faddeev ...
Cantini, Luigi +2 more
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Combinatorial Formula for the Hilbert Series of bigraded $S_n$-modules [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We introduce a combinatorial way of calculating the Hilbert series of bigraded $S_n$-modules as a weighted sum over standard Young tableaux in the hook shape case.
Meesue Yoo
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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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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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Orthogonality of Macdonald polynomials with unitary parameters [PDF]
Mathematische Zeitschrift, 2013 For any admissible pair of irreducible reduced crystallographic root systems, we present discrete orthogonality relations for a finite-dimensional system of Macdonald polynomials with parameters on the unit circle subject to a truncation relation.
J. F. van Diejen, E. Emsiz
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Haglund's conjecture for multi-t Macdonald polynomials
Discrete Mathematics, 2023 Title and abstract changed.
Seung Jin Lee +2 more
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Staircase Macdonald polynomials and the $q$-Discriminant [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We prove that a $q$-deformation $\mathfrak{D}_k(\mathbb{X};q)$ of the powers of the discriminant is equal, up to a normalization, to a specialization of a Macdonald polynomial indexed by a staircase partition. We investigate the expansion of $\mathfrak{D}
Adrien Boussicault, Jean-Gabriel Luque
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