Multiplication formula for Hernandez and Leclerc's quivers with potentials

TL;DR

This paper derives a multiplication formula for F-polynomials associated with Hernandez and Leclerc's quivers with potentials, linking it to the product of simple modules over quantum affine groups.

Contribution

It introduces a new multiplication formula for F-polynomials of specific quivers, connecting representation theory and quantum groups.

Findings

Derived a multiplication formula for F-polynomials

Connected F-polynomials to quantum affine group modules

Enabled description of simple module products

Abstract

In this paper, we study multiplication formula of $F$-polynomial of representations of Hernandez and Leclerc's quivers with potentials. Since the truncated $q$-characters of some real simple modules over a quantum affine group $U_q(\widehat{\mathfrak{g}})$ can be expressed in terms of such $F$-polynomials, one can describe the product of two simple modules over $U_q(\widehat{\mathfrak{g}})$ using this multiplication formula.