Universiteit Utrecht

Department of Mathematics

Special day on Lie groups: December 22, 2009

At the occasion of the thesis defense of Vincent van der Noort

Title thesis: Analytic parameter dependence of Harish-Chandra modules for real reductive Lie groups -- A family affair.
Date: Monday, December 21, 2009
Time: 14:30
Location: Academiegebouw, Domplein 29, Utrecht


Tuesday December 22

10:15 - 11:05: Bernhard Krötz (Hannover): Analytic factorization of Lie group representations
11:15 - 12:05: Eric Opdam (Amsterdam, UvA): Hecke algebras and the tempered L-function conjecture.
13:30 - 14:20: Henrik Schlichtkrull (Copenhagen): Analytic representations of Lie groups

Location: Buys Ballot Laboratory, Room 426.


  • Bernhard Krötz: For a Lie group representation G on a Frechet space E the Dixmier-Malliavin factorization theorem asserts that every smooth vector v in E can be written as a finite sum of f_i * v_i with v_i a smooth vector and f_i a test function on G. In this talk we report on recent work where we settle the factorization problem for analytic vectors in Lie group representations (joint with H. Gimperlein and C. Lienau).
  • Eric Opdam: This is a report on joint work with Volker Heiermann (NT.0908.0699). Let G be the a quasi-split reductive p-adic group. Shahidi defined local L-functions for ``generic'' smooth irreducible representations of G, and he conjectured that these L-functions are holomorphic in the right half-plane if the representation is tempered. We prove this conjecture in general by a reduction to affine Hecke algebras using Heiermann's support theorem for discrete series.
  • Henrik Schlichtkrull: The notion of an analytic representation of a Lie group is introduced. For reductive Lie groups, analytic globalizations of Harish-Chandra modules are studied. An important tool is the algebra of analytic superdecaying functions (joint with B. Krötz).

  • Last update: November 23, 2009.