Results 1 to 10 of about 18,484 (234)

Combinatorial Formulas for Macdonald and Hall-Littlewood Polynomials [PDF]

Discrete Mathematics & Theoretical Computer Science, 2009
A breakthrough in the theory of (type $A$) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of fillings of Young diagrams.
Cristian Lenart
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Macdonald Polynomials and Multivariable Basic Hypergeometric Series [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2007
We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent ...
Michael J. Schlosser
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On generalized Macdonald polynomials [PDF]

Journal of High Energy Physics, 2020
Generalized Macdonald polynomials (GMP) are eigenfunctions of specifically­deformed Ruijsenaars Hamiltonians and are built as triangular polylinear combinations of Macdonald polynomials.
A. Mironov, A. Morozov
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Quantum corner VOA and the super Macdonald polynomials [PDF]

Journal of High Energy Physics
In this paper, we establish a relation between the quantum corner VOA $$q{\widetilde{Y}}_{L,0,N}[\Psi ]$$ , which can be regarded as a generalization of quantum W N algebra, and Sergeev-Veselov super Macdonald polynomials.
Panupong Cheewaphutthisakun, Jun’ichi Shiraishi, Keng Wiboonton   +2 more
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A bijective proof of a factorization formula for Macdonald polynomials at roots of unity [PDF]

Discrete Mathematics & Theoretical Computer Science, 2008
We give a combinatorial proof of the factorization formula of modified Macdonald polynomials $\widetilde{H}_{\lambda} (X;q,t)$ when $t$ is specialized at a primitive root of unity.
F. Descouens, H. Morita, Y. Numata
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Combinatorial theory of Macdonald polynomials I: proof of Haglund's formula. [PDF]

Proc Natl Acad Sci U S A, 2005
Haglund J, Haiman M, Loehr N.
europepmc   +2 more sources

A combinatorial approach to Macdonald q, t-symmetry via the Carlitz bijection [PDF]

Discrete Mathematics & Theoretical Computer Science, 2020
We investigate the combinatorics of the symmetry relation H μ(x; q, t) = H μ∗ (x; t, q) on the transformed Macdonald polynomials, from the point of view of the combinatorial formula of Haglund, Haiman, and Loehr in terms of the inv and maj statistics on ...
Maria Monks Gillespie
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E-Polynomials of Generic $\mathbf {\operatorname {\mathrm {GL}}_n\rtimes \!<\!\sigma \!>\!}~$ -Character Varieties: Branched Case

Forum of Mathematics, Sigma, 2023
For any branched double covering of compact Riemann surfaces, we consider the associated character varieties that are unitary in the global sense, which we call $\operatorname {\mathrm {GL}}_n\rtimes \!}$ -character varieties.
Cheng Shu
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A representation-theoretic proof of the branching rule for Macdonald polynomials [PDF]

Discrete Mathematics & Theoretical Computer Science, 2015
We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of $U_q(gl_n)$. In the Gelfand-Tsetlin basis, we show that diagonal
Yi Sun
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Macdonald polynomials at $t=q^k$ [PDF]

Discrete Mathematics & Theoretical Computer Science, 2009
We investigate the homogeneous symmetric Macdonald polynomials $P_{\lambda} (\mathbb{X} ;q,t)$ for the specialization $t=q^k$. We show an identity relying the polynomials $P_{\lambda} (\mathbb{X} ;q,q^k)$ and $P_{\lambda} (\frac{1-q}{1-q^k}\mathbb{X} ;q ...
Jean-Gabriel Luque
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