Generating functions and multiplicity formulas: the case of rank two simple Lie algebras

Abstract

A procedure is described that makes use of the generating function of characters to obtain a new generating function $H$ giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from $H$ explicit multiplicity formulas for particular weights is explained and the results corresponding to rank two simple Lie algebras shown.

References in corpus (5)

• The fundamental role of symmetry in nuclear models
• Generating functions and multiplicity formulas: the case of rank two simple Lie algebras
• On the generating function of weight multiplicities for the representations of the Lie algebra $C_2$
• 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 (4)

• Generating functions and multiplicity formulas: the case of rank two simple Lie algebras
• Multiplicity formulas for fundamental strings of representations of classical Lie algebras
• The $q$-analog of Kostant's partition function and the highest root of the classical Lie algebras
• Euler's difference table and decomposition of tensor powers of adjoint representation of $A_n$ Lie algebra