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Journal of Lie Theory 22 (2012), No. 3, 817--838
Copyright Heldermann Verlag 2012

A New Character Formula for Lie Algebras and Lie Groups

Waldeck Schtzer
Universidade Federal de So Carlos, Departament of Mathematics, Rod. Washington Luis - Km 235, 13565-905 So Carlos, SP, Brazil

The aim of this paper is to present a new character formula for finite-dimensional representations of finite-dimensional complex semisimple Lie Algebras and compact semisimple Lie Groups. Some applications of the new formula include the exact determination of the number of weights in a representation, new recursion formulas for multiplicities and, in some cases, closed formulas for the multiplicities themselves.

Keywords: Representation theory, characters, multiplicities, recursions, Ehrhart polynomials.

MSC: 17B10; 33C50

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