Gaiotto Conjecture for $\mathrm{Rep}_q(\mathrm{F}(4))$

TL;DR

This paper advances the proof of the Gaiotto conjecture by establishing it for the exceptional quantum supergroup U_q(f(4)), extending previous results from general linear supergroups to this specific case.

Contribution

It provides the first proof of the Gaiotto conjecture for the exceptional quantum supergroup U_q(f(4)), completing the series of proofs for basic classical quantum supergroups.

Findings

Proof of the Gaiotto conjecture for U_q(f(4))

Extension of previous results from general linear supergroups

Establishment of structural properties of U_q(f(4))

Abstract

This paper is a part of the series proving the Gaiotto conjecture for basic classical quantum supergroups. The previous part arXiv:2107.02653 [math.RT] , arXiv:2306.09556 [math.RT], proved the Gaiotto conjecture for the general linear quantum supergroups $U_q(\mathfrak{gl}(N|M))$. Here we deal with the exceptional quantum supergroup $U_q(\mathfrak{f}(4))$.