Metroplex Algebraic Geometry, Algebra and Number
Theory (AGANT) Seminar, a joint venture of
UNT, UTA
and TCU
Date/Time/Room: Friday (10/19/2012) at 4:30 pm
in 311 Pickard Hall
Speaker: Prof. Charles
Conley,
Department of
Mathematics,
University of North Texas.
"Representations
of Vector Field Lie Algebras"
Abstract:This talk will be an introduction
to representations of
Lie algebras of vector fields on Euclidean spaces. We
will focus mainly on the simplest example, the Lie algebra
Vec(R) of vector fields on the line. Although this algebra
may be defined relatively simply, its representation theory
is intricate and has been the topic of a considerable amount
of research over the past two decades. Some of the important
objects in the area are the tensor density modules, which are
deformations of the natural action of Vec(R) on the space of
functions and yield all of the irreducible admissible modules,
and the differential operator modules, which provide examples
of cohomology classes "in nature". A crucial tool in studying
these representations is the projective subalgebra, which
consists of the infinitesimal linear fractional transformations
and is a copy of sl(2).
We will describe some of the results which have been obtained in
the 1dimensional case, and mention the status of the analogous
questions in higher dimensions, where much less is known. We will
try to make the talk accessible to nonspecialists and graduate
students: in particular, we will not assume any prior knowledge
of Lie algebras or their representations.
A map of UTA may be found at
http://www.uta.edu/maps/,
and at http://www.uta.edu/maps/transportation.
The former gives buildings and the latter gives parking lots; both
are interactive. Note that PKH is the triangular building in
the 3 pm position in the former. Select Pickard Hall from the
building selector. PKH is next to the ``garage'' & is on
Nedderman Dr between Planatarium Place (aka College St) & West
St. West St is oneway northbound between W Mitchell St and 3rd
St. Parking is available in the nearby (East and SE of PKH)
parking lots with a UTA permit (but many people park there late on
Fridays with no permit). There are a few metered parking spots on
the East side of Pickard Hall on West St. Visitor (free), &
metered, parking is available by Davis Hall (marked DH in SW part
of the submap). A parking garage (expensive) is nextdoor to PKH
(use West St to get to it). Note that if heading south on Cooper,
then no left turn is allowed to Nedderman Dr.
Note that PKH 311 is on the 3rd floor of PKH; turn LEFT out of
elevator on 3rd floor to end of hall, left again towards the end
of that hall, and 311 will be on your righthand side.
Questions, etc on arrangements/directions should be
sent to Dr Vancliff; if
travelling from out of town, notify Dr Vancliff, as we will delay
starting the talk for you if you are late.
