Young Walls of Type $D^{(}2{)}_n+1$ and Strict Partitions

Abstract

We show that the number of reduced Young walls of type $D_{n+1}^{(2)}$ with $m$ blocks is independent of $n$ and the same as the number of strict partitions of $m$. Thus the principally specialized character ${\chi }_n^{{\Lambda }_0}(t)$ of $V({\Lambda }_0)$ over $U_q(D_{n+1}^{(2)})$ can be interpreted as a generating function for strict partitions. Hence we obtain an infinite family of generalizations of Euler's partition identity.

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