Branching Rules and Tensor Product Decompositions in Algebraic Lie Theory

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9801442 Brundan This award supports research on the study and computation of various branching rules for modular representations of general linear groups and symmetric groups. In particular, the principal investigator is interested in determining to what extent such classical branching coefficients are equal to the analogous coefficients in the quantum versions of these problems. He hopes both to extend existing techniques based on lowering operators, and to exploit newly understood connections between branching rules and decompositions of tensor products. A parallel project is to generalize existing results on completely splittable representations for general linear groups to orthogonal and symplectic groups. The research supported concerns the representation theory of various algebraic objects including general linear groups and symmetric groups. Representation theory is an important method for determining the structure of these objects. This work has implications for a number of areas of mathematics including ring theory, group theory, topology and the study of Lie algebras.