Quantum Lobachevsky Spaces and Wave Functions of Relativistic Toda Lattice

Alexey Valerievich Shchepetilov

Anjan Kundu

A. Matsuyama

Antoine Duval, Vincent Pasquier

Abstract We use the Pieri rules to recover the q -boson model and show it is equivalent to a discretized version of the relativistic Toda chain. We identify its semi infinite transfer matrix and the corresponding Baxter Q -matrix with half vertex operators related by an ω -duality transformation. We observe that the scalar product of two higher spin XXZ wave functions can be expressed with a Gaudin determinant.

Kazuhiro Hikami

The quantum open Toda lattice is studied by the method of the separation of variable developed by Sklyanin. The quantum canonical operators are derived from the monodromy matrix. Discussed is also the relativistic open Toda lattice.

Franz G. Mertens, Manfred Hader