Results 11 to 20 of about 561,255 (240)

c-functions and Macdonald polynomials [PDF]

Journal of Algebra, 2022
This is a paper about $c$-functions and Macdonald polynomials. There are $c$-function formulas for $E$-expansions of $P_λ$ and $A_{λ+ρ}$, principal specializations of $P_λ$ and $E_μ$, for Macdonald's constant term formulas, and for the norms of Macdonald polynomials.
L. Colmenarejo, Arun Ram
semanticscholar   +5 more sources

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
doaj   +5 more sources

Canonical Basis and Macdonald Polynomials [PDF]

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 $q=t^2$.
Beck, Jonathan, Frenkel, Igor, Jing, Naihuan   +2 more
core   +5 more sources

Lusztig Varieties and Macdonald Polynomials [PDF]

Algebras and Representation Theory
This paper uses Lusztig varieties to give central elements of the Iwahori-Hecke algebra corresponding to unipotent conjugacy classes in the finite Chevalley group $$GL_n(\mathbb {F}_q)$$ G L n ( F q ) .
Arun Ram
semanticscholar   +3 more sources

Specializing Koornwinder polynomials to Macdonald polynomials of type B, C, D and BC

Journal of Algebraic Combinatorics, 2021
We study the specializations of parameters in Koornwinder polynomials to obtain Macdonald polynomials associated to the subsystems of the affine root system of type $$(C_n^\vee ,C_n)$$ ( C n ∨ , C n ) in the sense of Macdonald (Affine Hecke algebras and ...
Kohei Yamaguchi, S. Yanagida
semanticscholar   +3 more sources

A positivity result in the theory of Macdonald polynomials. [PDF]

Proc Natl Acad Sci U S A, 2001
Garsia AM, Haglund J.
europepmc   +3 more sources

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

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, Dimitri Lebedev, I.G. Macdonald, R.J. Baxter, R.P. Stanley, S.N.M. Ruijsenaars, Sergey Oblezin, V. Pasquier   +7 more
core   +8 more sources

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, de Gier, Jan, Wheeler, Michael   +2 more
core   +7 more sources

Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2009
We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which ...
Robin Langer, Michael J. Schlosser, S. Ole Warnaar   +2 more
doaj   +2 more sources