53 citations · 167 across the 9 of their papers we have counts for
9 papers
Baxter operator formalism for Macdonald polynomials
Anton Gerasimov, Dimitri Lebedev, Sergey Oblezin
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…
On a classical limit of q-deformed Whittaker functions
Anton Gerasimov, Dimitri Lebedev, Sergey Oblezin
We provide a derivation of the Givental integral representation of the classical -Whittaker function as a limit of the q-deformed -Whittaker fun…
On q-deformed gl(l+1)-Whittaker function III
Anton Gerasimov, Dimitri Lebedev, Sergey Oblezin
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…
On q-deformed gl(l+1)-Whittaker function
Anton Gerasimov, Dimitri Lebedev, Sergey Oblezin
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)…
On q-deformed gl(l+1)-Whittaker function II
Anton Gerasimov, Dimitri Lebedev, Sergey Oblezin
A representation of a specialization of a q-deformed class one lattice gl(\ell+1}-Whittaker function in terms of cohomology groups of line bundles on the space QM_d(P^{\ell}) of qu…
Baxter operator and Archimedean Hecke algebra
A. Gerasimov, D. Lebedev, S. Oblezin
In this paper we introduce Baxter integral Q-operators for finite-dimensional Lie algebras gl(n+1) and so(2n+1). Whittaker functions corresponding to these algebras are eigenfuncti…