Zobrazeno 1 - 10
of 44
pro vyhledávání: '"Lebedev, Dimitri"'
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 th
Externí odkaz:
http://arxiv.org/abs/1204.0926
The universal Baxter operator is an element of the Archimedean spherical Hecke algebra H(G,K), K be a maximal compact subgroup of a Lie group G. It has a defining property to act in spherical principle series representations of G via multiplication o
Externí odkaz:
http://arxiv.org/abs/1104.0420
We provide a derivation of the Givental integral representation of the classical $gl_{\ell+1}$-Whittaker function as a limit $q \to 1$ of the q-deformed $gl_{\ell+1}$-Whittaker function represented as a sum over the Gelfand-Zetlin patterns.
Comm
Comm
Externí odkaz:
http://arxiv.org/abs/1101.4567
Recently we propose a class of infinite-dimensional integral representations of classical gl(n+1)-Whittaker functions and local Archimedean local L-factors using two-dimensional topological field theory framework. The local Archimedean Langlands dual
Externí odkaz:
http://arxiv.org/abs/1011.2462
Publikováno v:
JHEP 1109:076,2011
Looking for a quantum field theory model of Archimedean algebraic geometry a class of infinite-dimensional integral representations of classical special functions was introduced. Precisely the special functions such as Whittaker functions and Gamma-f
Externí odkaz:
http://arxiv.org/abs/1011.0403
First, we define a generalization of the standard quantum Toda chain inspired by a construction of quantum cohomology of partial flags spaces GL(\ell+1)/P, P a parabolic subgroup. Common eigenfunctions of the parabolic quantum Toda chains are general
Externí odkaz:
http://arxiv.org/abs/1002.2622
In the first part of this series of papers we propose a functional integral representation for local Archimedean L-factors given by products of the Gamma-functions. In particular we derive a representation of the Gamma-function as a properly regulari
Externí odkaz:
http://arxiv.org/abs/0909.2016
We conjecture an explicit construction of integral operators intertwining various quantum Toda chains. Compositions of the intertwining operators provide recursive and Q-operators for quantum Toda chains. In particular we propose a generalization of
Externí odkaz:
http://arxiv.org/abs/0907.0299
We identify q-deformed gl(l+1)-Whittaker functions with a specialization of Macdonald polynomials. This provides a representation of q-deformed gl(l+1)-Whittaker functions in terms of Demazure characters of affine Lie algebra \hat{gl(l+1)}. We also d
Externí odkaz:
http://arxiv.org/abs/0805.3754
We propose new explicit form of q-deformed Whittaker functions solving q-deformed gl(l+1)-Toda chains. In the limit q->1 constructed solutions reduce to classical class one gl(l+1)-Whittaker functions in the form proposed by Givental. An important pr
Externí odkaz:
http://arxiv.org/abs/0803.0145