“Spread” Restricted Young Diagrams from a 2D WZNW Dynamical Quantum Group

Abstract

The Fock representation of the Q-operator algebra for the diagonal 2D ${\widehat{su}}(n)_k\,$ WZNW model where $Q=(Q_j^i), Q^i_j = a^i_\alpha \otimes \bar{a}^\alpha _j$, and $a^i_\alpha , \bar{a}^\beta _j$ are the chiral WZNW “zero modes”, has a natural basis labeled by su(n) Young diagrams $Y_\mathbf m\,$ subject to the “spread” restriction

$$\begin{aligned}\boxed {\mathrm{\text {spr}}\,(Y_\mathbf m):= \#(\text {columns}) +\#(\text {rows}) \le k+n =: h.}\end{aligned}$$