Novel energy preserving bijections between affine crystals for $U_q({\widehat{\mathfrak{sl}}}_2)$ and integer partitions

Sota Miyazawa, Taichiro Takagi

Let $B(\hat{I}{›}_a)(a=0,1)$ be the crystal of the level 1 integrable irreducible highest weight representation of the affine quantum group $U_q({\widehat{\mathfrak{sl}}}_2)$. We conside…