State sums for some super quantum link invariants

TL;DR

This paper develops state sum models for super quantum link invariants derived from the representation theory of quantum superalgebras, specifically relating to exterior powers of standard representations and their connection to Kashaev invariants.

Contribution

It introduces explicit state sum formulations for super quantum invariants and explores their relation to known invariants like Kashaev's.

Findings

State sum formulations for super quantum invariants.

Connection established between these invariants and Kashaev invariants.

Analysis focused on the N-th exterior power of the standard representation.

Abstract

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