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4:00 pm Wednesday, February 2, 2011 Stulken Geometry-Analysis Seminar: Asymptotics of Dimensions of Isotypic Components in Schur-Weyl Duality by
Sevak Mkrtchyan (Rice University) in HB 227- Vershik and Kerov in 1985 gave asymptotic bounds for the maximal and typical dimensions of the irreducible representations of the symmetric group. It was conjectured by Grigori Olshanski that the maximal and typical dimensions of the isotypic components of the representations in the base of Schur-Weyl duality accept similar asymptotic bounds. The isotypic components of this representation are parametrized by certain Young diagrams, and the relative dimensions of these components give rise to a measure on Young diagrams. Philippe Biane in 2001 found the limit shape of a typical Young diagram with respect to this measure. We will discuss a proof of the conjecture of Grigori Olshanski which is based on showing that the limit shape found by Biane is the minimizer of a certain functional.
Submitted by damanik@rice.edu |