The ${\mathfrak{sl}}_{\infty }$-crystal combinatorics of higher level Fock spaces

Thomas Gerber, Emily Norton

For integers $e,\ell \ge 2$, the level $\ell$ Fock space has an ${\mathfrak{sl}}_{\infty }$-crystal structure arising from the action of a Heisenberg algebra, intertwining the $\widehat…