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A Summation Formula for Macdonald Polynomials [PDF]
Letters in Mathematical Physics, 2016 We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases $t=1$ and $q=0$, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively.
de Gier, J, Wheeler, M
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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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(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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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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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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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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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
Jonathan Beck +2 more
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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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Macdonald polynomials and cyclic sieving [PDF]
European Journal of Combinatorics, 2022 A new result added, 13 ...
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