On the tensor product of two basic representations of $U_v({\widehat{sl}}_e)$

Susumu Ariki, Victor Kreiman, Shunsuke Tsuchioka

Let $\{B({\Lambda }_m)|m\in \mathbb{Z}/e\mathbb{Z}\}$ be the set of level one $\mathfrak{g}(A_{e-1}^{(1)})$-crystals, and consider the realization of $B({\Lambda }_m)$ using $e$-restricted partitions. We prove a pur…