# Representations of mutli-variable currents and a generalization of the Catalan and Narayana numbers

SPEAKER: Sergey Loktev

TITLE: Representations of mutli-variable currents and a generalization of the Catalan and Narayana numbers.

ABSTRACT For each partition we construct a natural representation of the Lie algebra of two-variable matrix-valued polynomials. We discuss universality properties of these repreresntations as well as combinatorics of their characters. We present an explicit answer for the case of partition $(n)$, when the dimension is the Fuss-Catalan number, as well as a simple recurrance relation in general case. At last we discuss possible generalizations for a bigger number of variables.