Quantum Supersymmetric Toda-mKdV Hierarchies

TL;DR

This paper extends the quantization of Toda-mKdV hierarchies to arbitrary affine superalgebras, introducing quantum monodromy matrices and L-operators, and demonstrating quantum integrability with key examples.

Contribution

It provides a general framework for quantizing Toda-mKdV hierarchies for affine superalgebras, including construction of monodromy matrices and L-operators.

Findings

Quantum monodromy matrix related to universal R-matrix introduced

Auxiliary L-operators satisfying RTT-relation constructed

Quantum integrability condition established

Abstract

In this paper we generalize the quantization procedure of Toda-mKdV hierarchies to the case of arbitrary affine (super)algebras. The quantum analogue of the monodromy matrix, related to the universal R-matrix with the lower Borel subalgebra represented by the corresponding vertex operators is introduced. The auxiliary L-operators satisfying RTT-relation are constructed and the quantum integrability condition is obtained. General approach is illustrated by means of two important examples.