Back to Departmental Colloquium: Spring 2012
Departmental Colloquium
Date: Thursday, Feb 9, 2012
Time: 4:15PM
Location: JWB 335
Eric Opdam
University of Amsterdam, Netherlands
Title |
Harmonic analysis on p-adic reductive groups and homological algebra |
Abstract |
The Fourier decomposition of an L^2-function on a p-adic semi simple group G contains contributions from spectral series of various dimensions. These spectral series consist of irreducible representations of G which have “moderate growth behavior at infinity’’, the so-called tempered irreducible representations. These tempered irreducible representations are therefore the relevant representations of G to consider when studying the harmonic analysis on G. Tempered representations also have striking algebraic properties. With Maarten Solleveld we have proved an explicit formula for the space of higher extensions between irreducible tempered representations. This has applications to the computation of the so-called elliptic pairing of admissible characters of G (the so-called “Kazhdan orthogonality conjecture’’). With Dan Ciubotaru and Peter Trapa we considered an explicit construction of the (limits of) discrete series as the index of a Dirac operator (for graded affine Hecke algebras). This gives an expression of the aforementioned elliptic pairing in terms of index theory. |
Number Theory
Representation Theory
Commutative Algebra