121 citations · 290 across the 15 of their papers we have counts for
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On topological field theory representation of higher analogs of classical special functions
Anton A. Gerasimov, Dimitri R. Lebedev
Looking for a quantum field theory model of Archimedean algebraic geometry a class of infinite-dimensional integral representations of classical special functions was introduced. P…
Parabolic Whittaker Functions and Topological Field Theories I
Anton Gerasimov, Dimitri Lebedev, Sergey Oblezin
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.…
Archimedean L-factors and Topological Field Theories II
Anton Gerasimov, Dimitri Lebedev, Sergey Oblezin
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 w…
Unitary representations of $U_{q}(\mathfrak{sl}(2,\RR))$, the modular double, and the multiparticle q-deformed Toda chains
S. Kharchev, D. Lebedev, M. Semenov-Tian-Shansky
The paper deals with the analytic theory of the quantum q-deformed Toda chain; the technique used combines the methods of representation theory and the Quantum Inverse Scattering M…
Integral representations for the eigenfunctions of quantum open and periodic Toda chains from QISM formalism
S. Kharchev, D. Lebedev
The integral representations for the eigenfunctions of particle quantum open and periodic Toda chains are constructed in the framework of Quantum Inverse Scattering Method (QIS…
Eigenfunctions of $GL(N,\RR)$ Toda chain: The Mellin-Barnes representation
S. Kharchev, D. Lebedev
The recurrent relations between the eigenfunctions for $GL(N,\RR)$ and $GL(N-1,\RR)$ quantum Toda chains is derived. As a corollary, the Mellin-Barnes integral representation for t…