State sums for some super quantum link invariants

Abstract

We present state sums for quantum link invariants arising from the representation theory of $U_q({\mathfrak{gl}}_{N\mid M})$. We investigate the case of the $N$th exterior power of the standard representation of $U_q({\mathfrak{gl}}_{N\mid 1})$ and make explicit the relation with Kashaev invariants.