Papers, articles, and lecture courses by Bill Casselman
(published, accepted, or submitted)
Representations of padic groups

Original Notes on admissible representations of padic groups.
These are the original notes written at the IAS
in June, 1974, with a major correction
suggested a couple of years later by Cartier
and a few other minor ones.
They were subsequently put into TEX
under Paul Sally's direction at the University of Chicago.
They contain a number of small mathematical errors.
The most egregious is the formulation of the BruhatTits KTK reduction.

On some results of Atkin and
Lehner,
Mathematische Annalen 201 (1973), 301314 (link to the Göttingen
archive)

The restriction of a representation of GL(2,k) to
GL(2,o),
Mathematische Annalen 206 (1973), 311318 (link to the Göttingen
archive)

The unramified principal series of padic groups I.
Compositio Mathematica 40 (1980), 387406 (link to NUMDAM)

The unramified principal series of padic groups II
(with Joe Shalika)
Compositio Mathematica 41 (1980), 207231 (link to NUMDAM)

A new nonunitarity argument for padic representations,
from the Journal of the Faculty of Science of the University of Tokyo 28 (1982), 907928.

Notes on padic Whittaker functions
This is a collection of notes and letters written by me
to Freydoon Shahidi in the course of putting together our joint paper.

On irreducibility
of standard modules for generic representations (with Freydoon Shahidi),
Annales scientifiques de l'École Normale Supérieure 31
(1998), 561589.
Representations of real groups

Characters and Jacquet modules
Mathematische Annalen 230 (1977), 101105.

The restriction of admissible representations to n
Mathematische Annalen 233 (1978), 193198.

Jacquet modules for real reductive groups
(pp. 557563 in the Proceedings of the ICM in Helsinki, 1978).

The asymptotic behaviour of matrix coefficients of admissible
representations (with Dragan Milicic)
Duke Mathematics Journal 49 (1982), 869930.

Canonical extensions of HarishChandra
modules to representations of G
Canadian Journal of Mathematics 41 (1989), 385438.

Bruhat filtrations and Whittaker vectors
(with Henryk Hecht and Dragan Milicic)
AMS Proceedings of Symposia in Pure Mathematics 68 (2000), 151190.

Verifying a conjecture of Kottwitz
Journal of Representation Theory 4 (2000)

Jacquet modules and the asymptotic behaviour of matrix coefficients
Based on a talk at the 2007 Purdue conference in honour of Freydoon Shahidi.

The letters to Jim Arthur
These are referred to in the previous paper.

Computations in real tori
In Representation theory of real groups,
Contemporary Mathematics, volume 472, AMS, 2007.
A remark on an algorithm
used, more or less, in Fokko du Cloux's ATLAS program.
Automorphic forms

Automorphic forms and a Hodge theory
for congruence subgroups of SL_{2}(Z),
pp. 108140 in
Lie group representations II
(proceedings of a conference at the University of Maryland),
Lecture Notes in Mathematics 1041, 1983.

L2 cohomology of arithmetic
quotients of real rank one.
From a conference on representations of real reductive groups in Park City, Utah.

Introduction to
L2 cohomology of arithmetic quotients.
From a conference on singularities at Tsukuba University.
These two papers represent work done jointly with Armand Borel
on Zucker's conjecture that was never published, since shortly afterwards
complete proofs of the conjecture appeared.
Nonetheless, the techniques might someday be of interest.
The point is to show how the calculation of local L2 cohomology can be represented as (g,K)
cohomology of locally L2 automorphic forms on link groups, for groups of rational rank one and two.
This is an analogue of the conjecture of Borel about ordinary cohomology that was proved
for SL(2) in the Hodge theory paper, and then for all arithmetic groups by Jens Franke.

Introduction to the Schwartz space of
Γ \G
Canadian Journal of Mathematics XLI (1989)

Extended automorphic forms on the upper halfplane
Mathematischen Annalen 296 (1993).
There are some silly errors in this. The exponent of π in
Riemann's function is s/2 not s/2, and the residue
of E_{s} is 1/2ξ(2), making the volume
of the quotient SL(2,Z)\H equal to π/3.

Geometric rationality of Satake compactifications
Australian Mathematical Lecture Series 9 (1997)
(the Roger Richardson memorial issue)

On the Plancherel measure for the
continuous spectrum of the
modular group
This is a minor revision of
a paper originally published in an A.M.S. volume dedicated to Goro Shimura.
The revisions correct a few minor typographical errors and (I hope) improve
clarity.

The Lgroup
(from a conference in Tokyo on class field theory).
There are many typographical errors in the publishd
version, and a few misstatements in this as well.
Alas.

Stability of lattices and the partition of
arithmetic quotients
Asian Journal of Mathematics
8
(2004)
(issue dedicated to Armand Borel)

Truncation exercises
Functional Analysis
VIII
(2003)

Harmonic analysis of the Schwartz space of Γ \
SL_{2}(R)
Contributions to automorphic forms, geometry,
and number theory,
Johns Hopkins Press,
2004

A conjecture on the analytical behaviour of Eisenstein series
Pure and Applied Mathematics Quarterly
1
(2005)
Coxeter groups
Structure of algebraic groups
Miscellaneous
