Seminar on representation theory
and reductive groups  Fall 2006
The ground rule of the seminar is that all
talks should be comprehensible to graduate students.
Not necessarily with details of proofs,
but references should be adequate.
For those graduate students interested in obtaining credit for this seminar,
it is Mathematics 620A, section 101.

Meetings: Tuesdays
 2:30  3:30 in Math Annex 1118
 3:30  Math Annex 1102
Schedule

September 19  Bill Casselman  The Lgroup.
Written after my lecture:
I had meant to talk about the Lgroup,
and in fact to cover essentailly what is in
the relevant section of
my notes on spherical functions (mentioned later), but wound up
talking about more elementary material.

September 26  Hesam  Finite groups of Lie type.
He writes in email,
"When I first
learned about linear algebraic groups one of the
hard parts was groups over a field which is not alg.
closed. I think a good exposition of what happens to
groups (or their root data) over finite fields is very
useful in that regard. Also later if we do the same for padic groups
it is nice to compare the results."

October 3 
Patrick Walls on the ring of adeles

October 10  Julia Gordon on unramified principal series,
mostly SL(2).

October 17  Michael LeBlanc, `The Bruhat decomposition'.

October 24  Hesaam  reductive groups over finite fields II

October 31  Patrick Walls  Adeles II

November 7  Me  on the construction of a group from its root datum.
By the way, "data" is plural, "datum" singular.
"These data", not "this data." So is "agenda":
"He has hidden agenda," not "a hidden agenda."
"Agenda" is literally "things to be acted upon."
But even so, the use of "root datum"
for an array of things is unfortunate.

November 14  Michael LeBlanc  local zeta functions.
Thsi will go over questions raised in Patrick's last talk.

November 21  Julia Gordon  TBA
References
Good for browsing to choose topics.
Structure of padic groups
 Robert Steinberg,
Lectures on Chevalley groups.
The .pdf file has been compressed with gzip,
and meant to be downloaded before opening.
This classic was originally a set of lecture notes
published by the mathematics department of Yale University.
It is posted here with Steinberg's generous permission,
but copyright remains with him. A copy taken from here
must be for personal use only.

Ian Macdonald  Spherical functions on groups of padic type, Madras, 1971.

Jacques Tits  Reductive groups over local fields,
in Proceedings of Symposia in Pure Mathematics 33.
Nearly all the proceedings of the Corvallis
conference are available on line at
http://www.ams.org/online_bks/pspum331/

Kenneth Brown  Buildings.

Arjeh Cohen, Scott Murray, and Don Taylor  Computing in groups of Lie type.

Arjeh Cohen and Scott Murray, Algorithm for Lang's theorem
Representation theory
Weyl groups and root systems
