The weight function for monomial crystals of affine type

TL;DR

This paper derives an explicit formula for the affine weight in Nakajima monomial crystals specifically for affine types A_n^{(1)} and B_3^{(1)}, advancing the understanding of their structure.

Contribution

It provides a new explicit expression for the affine weight in Nakajima monomial crystals for certain affine types, which was previously unknown.

Findings

Explicit formula for affine weight in type A_n^{(1)}

Explicit formula for affine weight in type B_3^{(1)}

Enhanced understanding of monomial crystal structures

Abstract

In this work, an expression for the affine weight is calculated for Nakajima monomial crystals in affine types $A_n^{(1)}$ and $B_3^{(1)}$.