Results 21 to 30 of about 18,484 (234)
Clustering properties of rectangular Macdonald polynomials [PDF]
, 2012 The clustering properties of Jack polynomials are relevant in the theoretical study of the fractional Hall states. In this context, some factorization properties have been conjectured for the $(q,t)$-deformed problem involving Macdonald polynomials.
Charles F. Dunkl, Jean-Gabriel Luque
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Multi-Macdonald polynomials [PDF]
Discrete Mathematics, 2020 We introduce Macdonald polynomials indexed by $n$-tuples of partitions and characterized by certain orthogonality and triangularity relations. We prove that they can be explicitly given as products of ordinary Macdonald polynomials depending on special alphabets.
Camilo González, Luc Lapointe
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Modified Macdonald Polynomials and Integrability [PDF]
Communications in Mathematical Physics, 2020 References corrected, explanations and examples ...
Alexandr Garbali, Michael Wheeler
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Type A partially-symmetric Macdonald polynomials [PDF]
Algebraic CombinatoricsWe construct type A partially-symmetric Macdonald polynomials P (λ∣γ) , where λ∈ℤ ≥0 n-k is a partition and γ∈ℤ ≥0 k is a composition. These are polynomials which are symmetric in the first n-k variables, but not necessarily in the final k variables. We establish their stability and an integral form defined using Young diagram statistics. Finally, we
Ben Goodberry
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A combinatorial formula for Macdonald polynomials [PDF]
Journal of the American Mathematical Society, 2005 We prove a combinatorial formula for the Macdonald polynomialH~μ(x;q,t)\tilde {H}_{\mu }(x;q,t)which had been conjectured by Haglund. Corollaries to our main theorem include the expansion ofH~μ(x;q,t)\tilde {H}_{\mu }(x;q,t)in terms of LLT polynomials, a new proof of the charge formula of Lascoux and Schützenberger for Hall-Littlewood polynomials, a ...
J. Haglund +2 more
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Macdonald–Koornwinder Polynomials [PDF]
, 2020 An overview of the basic results on Macdonald(-Koornwinder) polynomials and double affine Hecke algebras is given. We develop the theory in such a way that it naturally encompasses all known cases. Among the basic properties of the Macdonald polynomials we treat are the quadratic norm formulas, duality and the evaluation formulas.
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Matrix product and sum rule for Macdonald polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We present a new, explicit sum formula for symmetric Macdonald polynomials Pλ and show that they can be written as a trace over a product of (infinite dimensional) matrices. These matrices satisfy the Zamolodchikov– Faddeev (ZF) algebra.
Luigi Cantini +2 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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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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(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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