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Representation Theory of Real and p-adic Groups / Théorie des représentations des groupes réels et p-adiques
(Org: Jason Levy and/et Monica Nevins)


CLIFTON CUNNINGHAM, University of Calgary, Calgary, Alberta
On some depth-zero orbital integrals

We show how l-adic sheaves on the rigid analytic Lie algebra for a p-adic group may be used to associate orbital integrals to generalised Green's functions on the reductive quotient of a parahoric.

STEPHEN DEBACKER, Science Center 325, Harvard University, Cambridge, Massachusetts  02138, USA
Some applications of Bruhat-Tits theory to harmonic analysis

Beginning with the fundamental work of Allen Moy and Gopal Prasad, the elegant structure theory of Bruhat and Tits has played an increasingly important role in both the representation theory and harmonic analysis of reductive p-adic groups. In this talk, we shall review some of the basic results in the latter category and discuss work that is currently in progress.

JULEE KIM, University of Illinois at Chicago, USA
Character expansions and refined K-types

Let k be a p-adic field. Let G be the group of k-rational points of a connected reductive group defined over k. Let p be an irreducible admissible representation of G of positive depth. We find a new character expansion of the character cp, which depends on K-types contained in p. We also determine a G-domain where this expression is valid. This is a joint work with Fiona Murnaghan.

WENTANG KUO, Queen's University, Kingston, Ontario
Principal nilpotent orbits and reducible principal series

Let G be a split reductive p-adic group. In this talk, we will establish an explicit link between principal nilpotent orbits of G and the irreducible constituents of principal series of G. A geometric characterization of certain irreducible constituents is also provided. In addition, we can express the relation in terms of L-group objects.

JASON LEVY, University of Ottawa, Ottawa, Ontario
Invariance and Arthur's truncation

We will derive an alternative derivation of the Kudla-Rallis regularized Siegel-Weil formula, using Arthur truncation. We show that a simple criterion determines when the truncated integrals are invariant, and relate it to the assumptions of Kudla-Rallis on the relative sizes of the dual groups.

PAUL MEZO, The Fields Institute, Toronto, Ontario  M5T 3J1
The unitary dual for metaplectic coverings of general linear groups

Suppose F is a p-adic field containing the n-th roots of unity. A metaplectic covering of GL(r,F) is a non-trivial n-fold covering group of GL(n,F). We shall provide a classification of the irreducible unitary representations of these metaplectic coverings, and discuss an application to the automorphic representations of metaplectic coverings.

FIONA MURNAGHAN, University of Toronto, Toronto, Ontario
Distinguished supercuspidal representations

Let G be the F-rational points of a connected reductive F-group, where F is a p-adic field. Let H be the fixed points of an involution of G. A representation of G is said to be H-distinguished whenever there exists a nonzero H-invariant linear functional on the space of the representation. We will discuss distinguishedness of tame supercuspidal representations of G in terms of the inducing data defined by J.-K. Yu.

MONICA NEVINS, University of Ottawa, Ottawa, Ontario  K1N 6N5
Branching rules for principal series representations of p-adic SL(2)

The principal series representations of p-adic SL(2,k) are restricted to SL(2,O), where O denotes the integer ring in k. This subgroup represents one of the two conjugacy classes of maximal compact subgroups in SL(2,k). The decomposition of these restricted representations is described in terms of Shalika's classification by orbits of irreducible representations of SL(2,O).

ALFRED NOËL, The University of Massachusetts, Boston, Massachusetts  02125, USA
Maximal Tori of reductive centralizers of nilpotents in exceptional complex symmetric spaces

The maximal tori and normal triples that I shall describe in this talk arise naturally in the study of nilpotent orbits of Lie groups and play an important role in several problems such as: classification of nilpotent orbits of real Lie groups, description of admissible nilpotent orbits of real Lie groups, classification of spherical nilpotent orbits, determination of component groups of centralizers of nilpotents in symmetric spaces. I shall present a simple algorithm for computing such tori and discuss two of the above applications.

ERIC SOMMERS, University of Massachusetts-Amherst and IAS
Ideals in the nilradical of a Borel subalgebra

We study an equivalence relation on the set of ideals in the nilradical of a Borel subalgebra. This appears to be related to the Springer correspondence. It also has a connection with Kazhdan-Lusztig cells in the affine Weyl group and we will explain a theorem concerning this connection.

FERNANDO SZECHTMAN, University of Waterloo, Waterloo, Ontario  N2L 3G1
Weil representations of symplectic and unitary groups over finite local rings

Let O be the ring of integers of a local field, with maximal ideal P. Write Sp2n(R) for the symplectic group of rank 2n over the quotient ring R=O/Pl. The Weil representation W of Sp2n(R) is defined, its irreducible constituents are determined, their Clifford theory is elucidated, and their character fields and Schur indices are computed. A character formula for the restriction of W to the unitary group Un([`(R)]), [`(R)] a quadratic extension of R, is given.

YUANLI ZHANG, CRM, University of Montreal, Montreal, Quebec
R-groups and Aubert involutions

Let p be a generic discrete representation of a Levi subgroup of SO(2n+1)(F), where F is a p-adic field. Then the R-group of Arthur and the classical R-group of the Aubert involution of p are isomorphic. This is a join work with Ban.


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