Results 41 to 50 of about 18,484 (234)

On factorization of generalized Macdonald polynomials

The European Physical Journal C, 2016
A remarkable feature of Schur functions -- the common eigenfunctions of cut-and-join operators from $W_\infty$ -- is that they factorize at the peculiar two-parametric topological locus in the space of time-variables, what is known as the hook formula for quantum dimensions of representations of $U_q(SL_N)$ and plays a big role in various applications.
Ya. Kononov, А. Морозов
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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 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, B. Feigin, B.S. Shastry, F. Bergeron, I.G. Macdonald, I.G. Macdonald, J.-F. Fortin, J.R. Stembridge, L. Brink, Luc Lapointe, M. Haiman, Olivier Blondeau-Fournier, P. Desrosiers, P. Desrosiers, P. Desrosiers, P. Desrosiers, Patrick Desrosiers, Pierre Mathieu, S.N. Ruijsenaars, S.N. Ruijsenaars   +19 more
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Difference Macdonald-Mehta Conjecture [PDF]

, 1997
In the paper we formulate and verify a difference counterpart of the Macdonald-Mehta conjecture and its generalization for the Macdonald polynomials.
Cherednik, Ivan
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A raising operator formula for Macdonald polynomials

Forum of Mathematics, Sigma
We 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, M. Haiman, J. Morse, A. Pun, G. H. Seelinger   +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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Yangian Gelfand-Zetlin Bases, gl(N)-Jack Polynomials and computation of Dynamical Correlation Functions in the Spin Calogero-Sutherland Model [PDF]

, 1997
We consider the gl(N)-invariant Calogero-Sutherland Models with N=1,2,3,... in a unified framework, which is the framework of Symmetric Polynomials.
Uglov, Denis
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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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Vogel's universality and Macdonald dimensions

Nuclear Physics B
We discuss algebraic universality in the sense of P. Vogel for the simplest refined quantity, the Macdonald dimensions. The main known source of universal quantities is given by Chern-Simons theory.
Liudmila Bishler
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Symmetric and nonsymmetric Macdonald polynomials [PDF]

Annals of Combinatorics, 1999
AMS-Latex, 24 ...
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