Representation Theory Seminar
2009-2010
Fridays at 1:45pm in LCB 219

2008-2009: 2008-2009
2007-2008: 2007-2008 		E. Cartan H. Weyl I. M. Gelfand Harish Chandra A. Borel R. Langlands

Date
  Speaker
Title
September 25
 Peter Trapa
 Highest weight modules
October 2
 Matt Housley Peter-Weyl Theorem
November 6
 Dragan Milicic Matrix coefficients, Peter-Weyl theorem and 5th Hilbert problem
November 13
 Anthony Henderson (Sidney) Pieces of nilpotent cones for classical groups
November 20
 Dragan Milicic Matrix coefficients, Peter-Weyl theorem and 5th Hilbert problem, II
December 4
 Florian Herzig (Northwestern)

Maintained by Dan Ciubotaru.


November 6, 2009
Dragan Milicic
Title: Matrix coefficients, Peter-Weyl theorem and 5th Hilbert problem
Abstract:   This is an expository talk aimed at graduate students.

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November 13, 2009
Anthony Henderson
Title: Pieces of nilpotent cones for classical groups
Abstract:   The algebraic groups SO_{2n+1} and Sp_{2n} have dual root data, so one expects there to be close connections between them. However, the nilpotent orbits of SO_{2n+1} in its Lie algebra seem superficially different from those of Sp_{2n}. Lusztig observed that on each side the orbits can be lumped together into `special pieces' which correspond more closely. For example, the number of points defined over a finite field in each special piece for SO_{2n+1} is the same as that in the corresponding special piece for Sp_{2n}, as Lusztig showed by direct computation. I will explain a new approach to this phenomenon, in which the two nilpotent cones are related via the exotic nilpotent cone of Syu Kato. This is joint work with Pramod Achar (Louisiana State University) and Eric Sommers (University of Massachusetts).

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