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 commentarXiv admin note: text overlap with arXiv:1304.7203

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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 $\mathrm{Sp}(4)$