Seminar on representation theory
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.
and reductive groups - Fall 2006
For those graduate students interested in obtaining credit for this seminar,
it is Mathematics 620A, section 101.
- 2:30 - 3:30 in Math Annex 1118
- 3:30 - Math Annex 1102
September 19 - Bill Casselman - The L-group.
Written after my lecture:
I had meant to talk about the L-group,
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 e-mail,
"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 p-adic 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,
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
Good for browsing to choose topics.
Structure of p-adic 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 p-adic 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
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
Weyl groups and root systems