On the generating function of weight multiplicities for the representations of the Lie algebra $C_2$

TL;DR

This paper derives a generating function for weight multiplicities in irreducible representations of the Lie algebra C2, providing recurrence relations and a graphical method for their computation.

Contribution

It introduces a new generating function approach for weight multiplicities in C2 representations, along with recurrence relations and a graphical computation method.

Findings

Derived a generating function for weight multiplicities in C2

Established recurrence relations among multiplicities

Developed a graphical recipe for computing multiplicities

Abstract

We use the generating function of the characters of $C_2$ to obtain a generating function for the multiplicities of the weights entering in the irreducible representations of that simple Lie algebra. From this generating function we derive some recurrence relations among the multiplicities and a simple graphical recipe to compute them.