121 citations · 278 across the 9 of their papers we have counts for
9 papers
Quantum Toda Lattice: a Challenge for Representation Theory
Michael Semenov-Tian-Shansky
Quantum Toda lattice may solved by means of the Representation Theory of semisimple Lie groups, or alternatively by using the technique of the Quantum Inverse Scattering Method. A…
Poisson groups and differential Galois theory of Schroedinger equation on the circle
Ian Marshall, Michael Semenov-Tian-Shansky
We combine the projective geometry approach to Schroedinger equations on the circle and differential Galois theory with the theory of Poisson Lie groups to construct a natural Pois…
Integrable Systems and Factorization Problems
M. A. Semenov-Tian-Shansky
The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the…
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…
Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras I. The case of Virasoro algebra
E. Frenkel, N. Reshetikhin, M. A. Semenov-Tian-Shansky
We propose a q-difference version of the Drinfeld-Sokolov reduction scheme, which gives us q-deformations of the classical W-algebras by reduction from Poisson-Lie loop groups. We…
Quantum and Classical Integrable Systems
M. A. Semenov-Tian-Shansky
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algeb…