5 citations · 10 across the 6 of their papers we have counts for
6 papers · 1 filter
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 normalizers of maximal tori in classical Lie groups
A. A. Gerasimov, D. R. Lebedev, S. V. Oblezin
The normalizer of a maximal torus in a semisimple complex Lie group does not in general allow a presentation as a semidirect product of and the correspon…
Normalizers of maximal tori and real forms of Lie groups
Anton A. Gerasimov, Dmitry R. Lebedev, Sergey V. Oblezin
Given a complex connected reductive Lie group with a maximal torus , Tits defined an extension of the corresponding Weyl group . The extended group is…
New Integral Representations of Whittaker Functions for Classical Lie Groups
A. Gerasimov, D. Lebedev, S. Oblezin
We propose integral representations of the Whittaker functions for the classical Lie algebras sp(2l), so(2l) and so(2l+1). These integral representations generalize the integral re…