Fall, 2011
- Speaker Abid Ali, Rutgers University
- Title Congruence subgroups of lattices in rank 2
Kac-Moody groups over finite fields
- Time/place 9/30/2011, Friday, 11:45 am in Hill 705
- Abstract In this talk, I will present joint work with
Prof. Lisa Carbone. We define congruence
subgroups K_{U^-}, K_{B^-} and K_{P^-_1}
of U^-, B^- and P^-_1
as natural generalizations of the corresponding
notions for lattices in Lie groups. It is known that the groups U^-,
B^- and P^-_1 are non-uniform
lattice subgroups of G. When G is a complete rank 2 Kac-Moody group
over a finite field, G
is locally compact and totally disconnected. The subgroup B^- =
HU^- where H is a `diagonal
subgroup' and U^- is generated by all negative real root groups, P^-_1
= B^- \cup B^- w_1 B^- is the
standard parabolic subgroup of the negative BN-pair for G. Our
technique involves determining
graphs of groups presentations for U^-, B^- and P^-_1.
We explicitly construct the graphs of groups
for congruence subgroups K_{U^-}, K_{B^-} and K_{P^-_1}
of U^-, B^- and P^-_1 respectively.
- Speaker Dan Barbasch, Cornell University
- Title Unipotent representations for Sp(p,q) and O*(n)
- Time/place 10/14/2011, Friday, 11:45 am in Hill 705
- Abstract In this work, joint with P. Trapa,
we establish the unitarity of the unipotent representations
in the sense of Arthur or Adams-Barbasch-Vogan for the real
forms Sp(p,q) and O*(n). Unipotent representations are conjectured
to be the building blocks of the unitary fual of a reductive real
group. The techniques rely heavily on properties of the associated
cycle or asymptotic support of an admissible module.
- Speaker Jerry Goldin, Rutgers University
- Title Diffeomorphism Group Representations and Anyonic
Statistics
- Time/place 10/21/2011, Friday, 11:45 am in Hill 705
- Abstract I shall first review how a fundamental
approach to
quantum mechanics based on unitary representations of
diffeomorphism groups led to an early prediction of
anyonic statistics in (2+1)-dimensions, including
nonabelian anyons obtained by inducing from higher-dimensional
braid group representations. Then I shall point to some
analogous possibilities for infinite-dimensional configuration
spaces, including anyonic statistics for extended objects in
3-dimensional space.
- Speaker Antun Milas, State University of New York at Albany
- Title Some irregular representations of vertex algebras
- Time/place 10/28/2011, Friday, 11:45 am in Hill 705
- Abstract I'll be discussing constructions and properties of certain
"irregular" representations of non-rational vertex algebras. The main
motivation for this line of work comes from the AGT conjecture in
physics, relating 2d CFTs and certain 4d supersymmetric field
theories.
This talk is meant to be accessible to graduate students interested in
Lie theory.
- Speaker Daniele Rosso, University of Chicago
- Title Classic and mirabolic RSK correspondence for
partial flags
- Time/place 11/11/2011, Friday, 11:45 am in Hill 705
- Abstract The Robinson-Schensted-Knuth correspondence is
a purely combinatorial statement, but Steinberg and Spaltenstein
independently found that it relates the relative position of two
complete flags to the irreducible components of the flag variety
in which they lie. Travkin then gave an algorithm for the case of
'mirabolic' varieties of complete flags. We will see how to
generalize both results to the case of partial flags.
- Speaker Vladimir Retakh, Rutgers University
- Title A short proof of Kontsevich cluster conjecture
- Time/place 11/18/2011, Friday, 11:45 am in Hill 552 (the colloquium room of the
statistics department; note that the room
is changed from Hill 705 to Hill 552 on that day)
- Abstract We give an elementary proof of the Kontsevich conjecture
that asserts that the iterations of the noncommutative rational map
K_r:(x,y)-->(xyx^{-1},(1+y^r)x^{-1}) are given by noncommutative Laurent
polynomials. (Joint work with Arkady Berenstein)
- Speaker Haisheng Li, Rutgers University at Camden
- Title On certain notions of quantum vertex (operator) algebra
- Time/place 12/02/2011, Friday, 11:45 am in Hill 705
- Abstract In the literature, there have been several notions of
quantum vertex (operator) algebra. The very first, called deformed
chiral algebra, was introduced by E. Frenkel and N. Reshetikhin, while
the second, called quantum vertex operator algebra, was introduced by
P. Etingof and D. Kazhdan. Later, essentially following
Etingof-Kazhdan, we introduced a notion of quantum vertex algebra. In
this talk, I will discuss a connection between this particular theory
of quantum vertex algebras and the Frenkel-Reshetikhin theory. For
this talk, I shall sketch the basic definitions and no pre-knowledge
on quantum vertex algebras is assumed. I will emphasize the conceptual
aspect, minimizing the technical part.
- Speaker Corina Calinescu, Yale University
- Title Vertex-algebraic structure of representations of affine Lie algebras
- Time/place 12/09/2011, Friday, 11:45 am in Hill 705
- Abstract This talk is an overview of the known results and
open problems about the
principal subspaces of standard modules for certain untwisted and twisted
affine Lie algebras. We discuss vertex-algebraic structure of principal
subspaces and their fermionic characters. This is joint work with Jim Lepowsky
and Antun Milas.
The talk will be introductory.
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