Representation theory of the orthogonal group from a combinatorial point of view

Jeb Willenbring

Yale University

March 15,
refreshments at 3:45pm


In the first part of this talk I will address some problems in classical invariant theory from a combinatorial point of view. Consequences of Schur-Weyl duality, the theory of symmetric pairs and Roger Howe's theory of dual reductive pairs will serve as tools to connect the combinatorial ideas with invariant theory.

During the second part of the talk, research done in collaboration with Thomas Enright will be described. This work is based on results of Thomas Enright, Roger Howe and Nolan Wallach concerning unitary highest weight representations. Specifically, we will see how these results provide a modern context for the Littlewood restriction formula (which is a branching rule for decomposing finite dimensional representations of GL(n) into irreducible representations of an orthogonal or symplectic subgroup). This context provides a stronger formulation of Littlewood's result. The results from the second part of the talk shed light on the problems addressed in the first part.

Speaker's Contact Info: jeb.willenbring(at-sign)

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