31 citations · 36 across the 7 of their papers we have counts for
7 papers
The Hecke-Baxter operator: principal series representations
Anton A. Gerasimov, Dmitry R. Lebedev, Sergey V. Oblezin
Previously introduced the Hecke-Baxter operator is a one-parameter family of elements in the commutative spherical Hecke algebra $\mathcal{H}(GL_{\ell+1}(…
Global Hecke-Baxter operator
Anton A. Gerasimov, Dmitry R. Lebedev, Sergey V. Oblezin
We construct a global Hecke-Baxter operator for integrable systems of arithmetic type associated with the group . This is an element of a global Hecke algebra associated with…
The Hecke-Baxter operators via Heisenberg group extensions
A. A. Gerasimov, D. R. Lebedev, S. V. Oblezin
The Hecke-Baxter operator was introduced as an element of the -spherical Hecke algebra associated with the Gelfand pair $O_{\ell+1}\subset GL_…
On equivalence of the Mellin-Barnes and the Givental integral representations of the Whittaker functions
A. A. Gerasimov, D. R. Lebedev, S. V. Oblezin
We construct an integral transformation intertwining the Gelfand-Tsetlin and the (modified) Gauss-Givental realizations of principle series representations of gl(3). This provides…
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…
On a Gauss-Givental Representation of Quantum Toda Chain Wave Function
A. Gerasimov, S. Kharchev, D. Lebedev +1
We propose group theory interpretation of the integral representation of the quantum open Toda chain wave function due to Givental. In particular we construct the representation of…