Type: Seminar

Distribution: World

Expiry: 16 May 2024

CalTitle1: Algebra Seminar: Kostant’s V(rho) \otimes V(rho) conjecture: a tour via convex geometry

Auth: alexs@desktop-h8gjltm.staff.wireless.sydney.edu.au (ashe8718) in SMS-SAML

Sam Jeralds (University of Sydney) is speaking in the Algebra Seminar next week. We will go out for lunch after the talk. When: Friday 8 March, 12-1pm Where: Carslaw 175 Title: Kostant’s V(rho) \otimes V(rho) conjecture: a tour via convex geometry Abstract: For a semisimple, complex Lie algebra g, a classical question in representation theory asks how the tensor product V(lambda) \otimes V(mu) of two irreducible, highest weight representations V(lambda) and V(mu) decomposes. This is, in general, hard to predict for arbitrary lambda and mu. For the special case of lambda=mu=rho, the half-sum of the positive roots of g, Kostant made a conjecture which describes the irreducible components of V(rho) \otimes V(rho) easily and explicitly. In this talk, we’ll use Kostant’s conjecture as a toy example to motivate a link between branching problems in representation theory and convex geometry via families of polytopes. We also aim to describe recent work extending this conjecture to affine Kac-Moody Lie algebras (and other applications as time permits).

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