Representation Theory Seminar

Representation Theory Seminar
2009-2010
Fridays at 3:00pm in LCB 215

2008-2009: 2008-2009
2007-2008: 2007-2008

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)	The classification of irreducible mod p representations of a p-adic GL_n
February 5	Scott Crofts (UC Santa Cruz)	Two sided parameter space for nonlinear simply laced groups
April 2	Moshe Adrian (Maryland)	A new construction of the tame local Langlands correspondence for GL(n,F), n a prime
May 17	Boris Sirola (Zagreb)	TBA (The room is LCB 222 at 2pm.)

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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December 4, 2009
Florian Herzig
Title: The classification of irreducible mod p representations of a p-adic GL_n
Abstract: Let F be a finite extension of the p-adic numbers. We describe the classification of irreducible admissible smooth representations of GL_n(F) over an algebraically closed field of characteristic p, in terms of "supersingular" representations. This generalizes results of Barthel-Livne for n = 2. Our motivation is the hypothetical mod p Langlands correspondence for GL_n, which is supposed to relate smooth mod p representations to Galois representations.

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April 2, 2010
Moshe Adrian
Title: A new construction of the tame local Langlands correspondence for GL(n,F), n a prime
Abstract: In my thesis, I give a new construction of the tame local Langlands correspondence for GL(n,F), n a prime. The Local Langlands Correspondence for GL(n,F) has been proven recently by Henniart, Harris/Taylor. In the tame case, supercuspidal representations correspond to characters of elliptic tori, but the local Langlands correspondence is unnatural because it involves a twist by some character of the torus. Taking the cue from the theory of real groups, supercuspidal representations should instead be parameterized by characters of covers of tori. DeBacker has calculated the distribution characters of supercuspidal representations for GL(n,F), n prime, and they are written in terms of functions on elliptic tori. Over the reals, Harish-Chandra parameterized discrete series representations of real groups by describing their distribution characters restricted to compact tori. Those distribution characters are written down in terms of functions on a canonical double cover of real tori. I have succeeded in showing that if one writes down a natural analogue of Harish-Chandra's distribution character for p-adic groups, it is the character of a unique supercuspidal representation of GL(n,F), where n is prime, far away from the identity. These results pave the way for a new, more natural, realization of the local Langlands correspondence for GL(n,F), n prime. In particular, there is no need to introduce any character twists.

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