258 citations · 625 across the 30 of their papers we have counts for
11 papers · 1 filter
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 quantum -Toda chain
A. A. Gerasimov, D. R. Lebedev, S. V. Oblezin
The orthosymplectic super Lie algebra is the closest analog of standard Lie algebras in the world of super Lie algebras. We demonstrate that the corresp…
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…
On universal Baxter operator for classical groups
Anton A. Gerasimov, Dimitri R. Lebedev
The universal Baxter operator is an element of the Archimedean spherical Hecke algebra H(G,K), K be a maximal compact subgroup of a Lie group G. It has a defining property to act i…
Quantum Toda Chains Intertwined
Anton Gerasimov, Dimitri Lebedev, Sergey Oblezin
We conjecture an explicit construction of integral operators intertwining various quantum Toda chains. Compositions of the intertwining operators provide recursive and Q-operators…
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…
On Baxter Q-operators And Their Arithmetic Implications
A. Gerasimov, D. Lebedev, S. Oblezin
We consider Baxter Q-operators for various versions of quantum affine Toda chain. The interpretation of eigenvalues of the finite Toda chain Baxter operators as local Archimedean L…
Baxter Q-operator and Givental integral representation for C_n and D_n
A. Gerasimov, D. Lebedev, S. Oblezin
Recently integral representations for the eigenfunctions of quadratic open Toda chain Hamiltonians for classical groups was proposed. This representation generalizes Givental repre…