"Spread" restricted Young diagrams from a 2D WZNW dynamical quantum group

TL;DR

This paper investigates the finite-dimensional Fock representation of the Q-operator algebra in the SU(n) WZNW model, revealing a basis labeled by Young diagrams with bounded spread, linking quantum groups and combinatorial structures.

Contribution

It introduces a finite-dimensional Fock space representation for the Q-operator algebra in the SU(n) WZNW model, characterized by Young diagrams with limited spread.

Findings

Fock representation is finite dimensional

Basis labeled by Young diagrams with spread ≤ k+n

Connects quantum group structure with combinatorial diagrams

Abstract

The Fock representation of the Q-operator algebra for the diagonal WZNW model on SU(n) at level k, where Q is the matrix of the 2D WZNW "zero modes" generating certain dynamical quantum group, is finite dimensional and has a natural basis labeled by su(n) Young diagrams Y of "spread" not exceeding h := k+n (spr (Y) = #(columns) + #(rows))