53 citations · 189 across the 25 of their papers we have counts for
28 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…
On a matrix element representation of the GKZ hypergeometric functions
A. A. Gerasimov, D. R. Lebedev, S. V. Oblezin
We develop a representation theory approach to the study of generalized hypergeometric functions of Gelfand, Kapranov and Zelevisnky (GKZ). We show that the GKZ hypergeometric func…
On a matrix element representation of special functions associated with toric varieties
A. A. Gerasimov, D. R. Lebedev, S. V. Oblezin
We develop representation theory approach to the study of special functions associated with toric varieties. In particular we show that the corresponding special functions are give…