Mathematical Sciences: Lie and Nonassociative Algebras

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This project is concerned with centralizer algebras, insertion schemes, stability and constructions of graded Lie algebras. The principal investigator will study tensor products of representations of complex simple Lie algebras and the behavior of spinor representations as the rank of the orthogonal Lie algebra goes to infinity. In addition, she will study constructions of graded Lie algebras as a means of systematically exploring simple Lie algebras of small characteristic and of determining root multiplicities for GIM and Kac-Moody algebras. This project is on the interface of physics, combinatorics, algebraic geometry and characteristic p algebra. It involves constructive representation questions left hanging since the time of Weyl and Brauer. These questions are presently of great interest to combinatorialists and physicists.