1,515 research outputs found
Factorization formulas for Macdonald polynomials
The aim of this note is to give some factorization formulas for different
versions of the Macdonald polynomials when the parameter t is specialized at
roots of unity, generalizing those existing for Hall-Littlewood functions
Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions
We study five dimensional AGT correspondence by means of the q-deformed
beta-ensemble technique. We provide a special basis of states in the q-deformed
CFT Hilbert space consisting of generalized Macdonald polynomials, derive the
loop equations for the beta-ensemble and obtain the factorization formulas for
the corresponding matrix elements. We prove the spectral duality for Nekrasov
functions and discuss its meaning for conformal blocks. We also clarify the
relation between topological strings and q-Liouville vertex operators.Comment: 22 pages, 1 figure, v2: typos corrected, a reference adde
On Factorization of Generalized Macdonald Polynomials
A remarkable feature of Schur functions -- the common eigenfunctions of
cut-and-join operators from -- 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
and plays a big role in various applications. This factorization
survives at the level of Macdonald polynomials. We look for its further
generalization to {\it generalized} Macdonald polynomials (GMP), associated in
the same way with the toroidal Ding-Iohara-Miki algebras, which play the
central role in modern studies in Seiberg-Witten-Nekrasov theory. In the
simplest case of the first-coproduct eigenfunctions, where GMP depend on just
two sets of time-variables, we discover a weak factorization -- on a
codimension-one slice of the topological locus, what is already a very
non-trivial property, calling for proof and better understanding.Comment: 8 page
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