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

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).