


Representation Theory of Real and padic Groups / Théorie
des représentations des groupes réels et padiques (Org: Jason Levy and/et Monica Nevins)
 HEATHER BETEL, Toronto
[PDF] 
 CLIFTON CUNNINGHAM, University of Calgary, Calgary, Alberta
On some depthzero orbital integrals
[PDF] 
We show how ladic sheaves on the rigid analytic Lie algebra for a
padic 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 BruhatTits theory to harmonic analysis
[PDF] 
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 padic 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 Ktypes
[PDF] 
Let k be a padic field. Let G be the group of krational
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 c_{p}, which
depends on Ktypes contained in p. We also determine a Gdomain
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
[PDF] 
Let G be a split reductive padic 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
Lgroup objects.
 JASON LEVY, University of Ottawa, Ottawa, Ontario
Invariance and Arthur's truncation
[PDF] 
We will derive an alternative derivation of the KudlaRallis
regularized SiegelWeil formula, using Arthur truncation. We show that
a simple criterion determines when the truncated integrals are
invariant, and relate it to the assumptions of KudlaRallis 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
[PDF] 
Suppose F is a padic field containing the nth roots of unity.
A metaplectic covering of GL(r,F) is a nontrivial nfold
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
[PDF] 
Let G be the Frational points of a connected reductive Fgroup,
where F is a padic field. Let H be the fixed points of an
involution of G. A representation of G is said to be
Hdistinguished whenever there exists a nonzero Hinvariant
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
padic SL(2)
[PDF] 
The principal series representations of padic 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
[PDF] 
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 MassachusettsAmherst and IAS
Ideals in the nilradical of a Borel subalgebra
[PDF] 
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 KazhdanLusztig 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
[PDF] 
Let O be the ring of integers of a local field, with
maximal ideal P. Write Sp_{2n}(R) for the symplectic
group of rank 2n over the quotient ring R=O/P^{l}. The Weil representation W of Sp_{2n}(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 U_{n}([`(R)]), [`(R)] a quadratic extension
of R, is given.
 YUANLI ZHANG, CRM, University of Montreal, Montreal, Quebec
Rgroups and Aubert involutions
[PDF] 
Let p be a generic discrete representation of a Levi subgroup of
SO(2n+1)(F), where F is a padic field. Then the Rgroup of
Arthur and the classical Rgroup of the Aubert involution of p
are isomorphic. This is a join work with Ban.

