Annotated Background Reading List:
In preparation for this summer's workshop, we
put together the following list of suggested background
reading. When possible we tried to find references which were
freely available online.
Based root data. The starting point
for much of the computational theory discussed in the workshop
is the classification of connected reductive complex algebraic groups
in terms of root data.
Some familiarity with these ideas is really prerequisite to most of the
A good reference for this material is T.A. Springer's Linear
Algebraic Groups (second edition) published in 1998 by Birkhauser in
their Progress in Math series, particularly Chapters 7-10. An (incomplete)
preview is available. A short
account (available freely online) of some of the main ideas is
available from Yiannis Sakellaridis.
A treatment of based root data in the (equivalent) setting of
connected compact Lie groups is contained in
Section 2 of the expository paper Three-dimensional subgroups and unitary representations by David
Vogan. Ideally this should be read in conjunction with Springer's account.
A nice self-contained exposition (a la Bourbaki) of the abstract
theory of root systems is in Section 5.1 (beginning on page 139)
of Dragan Milicic's notes
on Lie groups.
- The Bruhat decomposition.
Another essential prerequisite is familiarity with the
Bruhat decomposition. This is Section 8.3 in Springer's book
(We had trouble locating a complete online reference. Let us
know if you find one.)
- Background on Harish-Chandra modules. Some familiarity
with Harish-Chandra modules, as well as an acquaintance
with the representation theory of SL(2,R), would be very helpful.
Chapter 0 (particularly
Section 3) and Chapter 1 of David Vogan's green book
Representations of Real Reductive Lie Groups (published in 1981
by Birkhauser) are good places to start. The first twenty pages of the
Representations of semisimple Lie groups by Tony Knapp
and Peter Trapa also contains
a quick overview of the study of Harish-Chandra modules.
- Background on Kazhdan-Lusztig theory.
As preparation for the lectures of Stembridge and Trapa, it would be useful
to have taken at least a peek at Kazhdan and Lusztig's orginal
paper "Representations of Coxeter groups and Hecke algebras",
Inv. Math, vol 53, number (2), 165-184. A reasonable
account exists on