Essays on representations and automorphic forms by Bill Casselman

• Langlands' Fundamental Lemma for SL(2)
  Started out as informal notes to accompany a talk at TIFR, February 2009. I have now broken it up into pieces, which are still under construction:
  • The origins of endoscopy in a paper of Erich Hecke
  • Notes on the Bruhat-Tits tree (incomplete)
• Notes on spherical functions
  Written to accompany a reprinting of Ian Macdonald's book that has not materialized.

Real groups

• Structure
  • Maximal compact subgroups
• Representations
  • Continuous representations
  • Weyl's character formula and n-homology
  • The theorem of Dixmier-Malliavin
  • Admissible representations of SL(2,R)

Automorphic forms

• Automorphic forms for SL(2)
  • Geometry of the upper half plane
  • Arithmetic subgroups
  • Classical and adelic automorphic forms
  • Stereographic projection

Coxeter groups

• Reflections (June 19, 2012)
• Bruhat closures (July 1, 2012)
• Hecke algebras (February 10, 2012)
• The algorithm of Robinson-Schensted-Knuth (July 10, 2012)
• Coxeter elements (June 19, 2012)
• Kazhdan-Lusztig polynomials (July 1, 2012)

Analysis

• The Fourier transform
• The Gamma function
• Fourier Series and elliptic regularity
• Introduction to topological vector spaces
• Quasi-complete vector spaces
• A theorem of Émile Borel
• Integration on real manifolds

Algebra

• Representations of finite groups
• Partitions and nilpotent matrices
• Introduction to Lie algebras
• Jordan decompositions