Cohomology and representation theory for finite Lie groups
June 25 to June 29, 2007
at the
American Institute of Mathematics,
San Jose, California
organized by
Christopher Bendel,
Terrell Hodge,
Brian Parshall,
and Cornelius Pillen
Original Announcement
This workshop will be centered on the
prospects and potential for treating problems in the modular
representation theory and cohomology of finite groups of Lie type
via computational methods. Investigating applications of this
research and related topics to problems outside the field is an
associated goal.
The workshop thus aims to bring together two groups:
- those with
research interests related to the modular representation theory and
cohomology of finite groups of Lie type;
- experts in computation and applications whose experience may or
may not lie directly in the field, but whose knowledge could add
depth to the pool of ideas for this group.
Motivating aspects for the workshop include:
- New developments on the theoretical front, such as the recent
work on the Broue conjecture, which may have important
implications for the representation theory of the finite groups of
Lie type.
- The presence of fundamental theorems, in both defining and
cross-characteristic cases, which have have yet to be exploited by
powerful computational techniques.
- The rapid development and increasing sophistication of modules
for computational algebra packages, such as GAP, and growing use of
algebraic approaches to mathematical modeling, e.g., via Groebner
bases.
- Promising new
results that have arisen from other contexts (e.g., a new program
for computing Kazhdan-Lusztig polynomials by the ATLAS project on
Lie groups), mandating an examination of their suitability and/or
adaptability to the modular theory for finite groups of Lie type.
- Developments in technology and
computational packages over the last decade, coupled with
theoretical advances in the field, that have made portions of many
problems more amenable to adaptation as student research projects,
even with students possessing relatively modest backgrounds in
algebra.
Through small working groups, demonstrations, large-group
discussions, and some lectures, the workshop aims to:
- Assess the current state of past, present, and potential uses
for computation in the field, and to identify, assemble, and discuss
a list of problems for which progress might significantly hinge on
intensified computation.
- Fill in the lack of awareness on computational methods as a
tool for
theoretical advances on the part of some active researchers (and
potential researchers).
- Take steps to address other barriers to employing computational
methods, such as
- the lack of computational expertise on the part of researchers;
- lack of time/manpower to implement computational approaches;
- limitations on individual computing facilities;
- limitations on available algorithms, software, and programming
methods.
- Generate for researchers some awareness of potential
applications of their work to applied issues.
- Develop collaborative strategies among researchers and potential
researchers at various locations ranging from primarily
undergraduate institutions to research intensive universities.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
Workshop notes
Monday
l-modular representations of finite reductive groups by B. Srinivasan
Introduction to Kazhdan-Lusztig polynomials(Second half of Lin's lecture) (photos)
Monday afternoon discussion I (typed up)
Monday afternoon discussion II (modified version)
Monday discussion (directory of photos)
Tuesday
The Atlas of Lie groups and representations: Character Table by A. Noel
Calculating cohomology by J. Carlson
Computing (with) characters and respresentations by F. Luebeck
Wednesday
Website for the software LiE
demo.txt Magma demonstration file by D.Roozemond
demo_defs.txt Magma demonstration file by D.Roozemond
magma1.txt Transcript of demonstration given by D.Roozemond(1 of 2).
magma2.txt Transcript of demonstration given by D.Roozemond(2 of 2).
Cohomology of finite groups by R. Guralnick
Reduced standard modules and cohomology by L. Scott
Thursday
Group Photo I
Group Photo II
Group Photo III
Categorification by B. Srinivasan and P. Webb
An introduction to the cohomology and modular representation theory of the symmetric group by D. Hemmer
LiE.txt a demonstration of the software LiE by D. Roozemond
Photo 1
Photo 2
Photo 3
Photo 4
Photo 5
Photo 6
Photo 7
Photo 8
Photo 9
Photo 10
Photo 11
Photo 12
Photo 13
Photo 14
Photo 15
Friday
Georgia VIGRE Group
qua6-25.txt Gap demonstration (QuaGroup package) by C. Bendel
Photo 16
Photo 17
Photo 18
Photo 19
Photo 20
Photo 21
Photo 22
Photo 23
Photo 24
Photo 25
Photo 26
Photo 27
Photo 28
Photo 29
Photo 30
Photo 31
Photo 32
Useful information
Schur algebra calculations by J. Carlson (motivated by workshop problem sessions)
The latest stand alone package Coxeter 3 by Fokko Du Cloux
GAP lessons by P. Webb
Irreducible Modular Representations of
Finite and Algebraic Groups Notes by Christopher Drupieski and Terrell Hodge,
based on lectures by Leonard Scott.
The organizers have begun a wiki with a bibliography and reference
material, located at http://modularrepresentations.wetpaint.com/.
That wiki is viewable by anyone and can easily be edited.
Instructions for Downloading GAP
Papers arising from the workshop:
