The weight function for monomial crystals of affine type

ABSTRACT

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

KEYWORDS:

• Affine root system
• crystal
• Nakajima monomial

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 05E10
• 17B37

Acknowledgments

The authors would like to thank Sidney Graham and Meera Mainkar for their comments on an earlier version of this manuscript which was the first author’s Master’s thesis. The authors would also like to thank Jeong-Ah Kim, Kyu-Hwan Lee, Travis Scrimshaw, and Dong-Uy Shin for valuable conversations, detailed comments, and encouragement.