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

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.

arXiv admin note: text overlap with arXiv:1304.7203

References in corpus (3)

• The fundamental role of symmetry in nuclear models
• On an approach for computing the generating functions of the characters of simple Lie algebras
• On character generators for simple Lie algebras

Cited by in corpus (3)

• Generating functions and multiplicity formulas: the case of rank two simple Lie algebras
• Multiplicity formulas for fundamental strings of representations of classical Lie algebras
• A Density Theorem for $\mathrm{Sp}(4)$