Results 11 to 20 of about 18,484 (234)
Highest weight Macdonald and Jack polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2011 Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group.
Th. Jolicœur, Jean-Gabriel Luque
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Matrix product formula for Macdonald polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 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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Factorisation of Macdonald polynomials [PDF]
, 1997 We discuss the problem of factorisation of the symmetric Macdonald polynomials and present the obtained results for the cases of 2 and 3 variables.Comment: 13 pages, LaTex, no ...
Kuznetsov, Vadim B. +1 more
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Baxter operator formalism for Macdonald polynomials [PDF]
Letters in Mathematical Physics, 2013 We develop basic constructions of the Baxter operator formalism for the Macdonald polynomials associated with root systems of type A. Precisely we construct a dual pair of mutually commuting Baxter operators such that the Macdonald polynomials are their ...
Anton Gerasimov +7 more
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A combinatorial model for the Macdonald polynomials. [PDF]
Proc Natl Acad Sci U S A, 2004 We prove a combinatorial formula for the Macdonald polynomial H_mu(x;q,t) which had been conjectured by the first author. Corollaries to our main theorem include the expansion of H_mu(x;q,t) in terms of LLT polynomials, a new proof of the charge formula ...
Haglund J.
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Branching formula for Macdonald–Koornwinder polynomials [PDF]
Journal of Algebra, 2015 8 pages ...
J. F. van Diejen, E. Emsiz
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A Conjecture about Raising Operators for Macdonald Polynomials [PDF]
, 2005 A multivariable hypergeometric-type formula for raising operators of the Macdonald polynomials is conjectured. It is proved that this agrees with Jing and Jozefiak's expression for the two-row Macdonald polynomials, and also with Lassalle and Schlosser's
Jun’ichi Shiraishi
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Deformed Macdonald-Ruijsenaars Operators and Super Macdonald Polynomials [PDF]
Communications in Mathematical Physics, 2009 It is shown that the deformed Macdonald-Ruijsenaars operators can be described as the restrictions on certain affine subvarieties of the usual Macdonald-Ruijsenaars operator in infinite number of variables. The ideals of these varieties are shown to be generated by the Macdonald polynomials related to Young diagrams with special geometry.
A. N. Sergeev, А. П. Веселов
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Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials [PDF]
Selecta Mathematica, 2022 We present several new and compact formulas for the modified and integral form of the Macdonald polynomials, building on the compact "multiline queue" formula for Macdonald polynomials due to Corteel, Mandelshtam and Williams. We also introduce a new quasisymmetric analogue of Macdonald polynomials. These quasisymmetric Macdonald polynomials refine the
Corteel, Sylvie +4 more
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Factorizations of Symmetric Macdonald Polynomials [PDF]
Symmetry, 2018 We prove many factorization formulas for highest weight Macdonald polynomials indexed by particular partitions called quasistaircases. Consequently, we prove a conjecture of Bernevig and Haldane stated in the context of the fractional quantum Hall effect theory.
Laura Colmenarejo +2 more
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