title: Signature quantization and representations of compact Lie groups.
abstract: We discuss some applications of signature quantization to the representation theory of compact Lie groups. In particular, we prove signature analogues of the Kostant formula for weight multiplicities and the Steinberg formula for tensor product multiplicities. Using symmetric functions, we also find, for type A, analogues of the Weyl branching rule and the Gel'fand-Tsetlin theorem.
authors.affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, 02139, USA.
authors.forename: Victor
authors.initials: V
authors.lastname: Guillemin
authors.forename: Etienne
authors.initials: E
authors.lastname: Rassart