Papers, articles, and lecture courses by Bill Casselman
(published, accepted, or submitted)

Representations of p-adic groups

• Original Notes on admissible representations of p-adic groups.
  • Introduction to admissible representations of p-adic 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 Bruhat-Tits KTK reduction.
• On some results of Atkin and Lehner, Mathematische Annalen 201 (1973), 301-314 (link to the Göttingen archive)
• The restriction of a representation of GL(2,k) to GL(2,o), Mathematische Annalen 206 (1973), 311-318 (link to the Göttingen archive)
• The unramified principal series of p-adic groups I. Compositio Mathematica 40 (1980), 387-406 (link to NUMDAM)
• The unramified principal series of p-adic groups II (with Joe Shalika) Compositio Mathematica 41 (1980), 207-231 (link to NUMDAM)
• A new non-unitarity argument for p-adic representations, from the Journal of the Faculty of Science of the University of Tokyo 28 (1982), 907-928.
• Notes on p-adic 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), 561--589.
• Symmetric powers and the Satake transform. Contributed to an issue of the Bulletin of the Iranian Mathematical Society in honor of Freydoon Shahidi.

Representations of real groups

• Characters and Jacquet modules
  Mathematische Annalen 230 (1977), 101-105.
• The restriction of admissible representations to n
  Mathematische Annalen 233 (1978), 193-198.
• Jacquet modules for real reductive groups
  (pp. 557-563 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), 869-930.
• Canonical extensions of Harish-Chandra modules to representations of G
  Canadian Journal of Mathematics 41 (1989), 385-438.
• Bruhat filtrations and Whittaker vectors (with Henryk Hecht and Dragan Milicic)
  AMS Proceedings of Symposia in Pure Mathematics 68 (2000), 151-190.
• 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 SL₂(Z), pp. 108--140 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 half-plane
  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 L-group
  (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 \ SL₂(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

• Automata to perform basic calculations in Coxeter groups
  C.M.S. Conference Proceedings 16 (1994)
• Computation in Coxeter groups I. Multiplication
  Electronic Journal of Combinatorics 9 (2002)
• Computation in Coxeter groups II. Constructing minimal roots
  Journal of Representation Theory 12 (2008)
• The CRM course on Coxeter groups
• A CRM lecture

Structure of algebraic groups

• The computation of structure constants according to Jacques Tits
  A practical explanation of how to use Tits' work on structure constants to compute them.
• On Chevalley's formula for structure constants in the Journal of Lie Theory 25(2) (2015).

Miscellaneous

• Review of the book on Eisenstein series by Moeglin and Waldspurger
  (a review for the Bulletin of the AMS)