Geometry of the smooth dual of GL(n)
K-Theory and Homology
2009-10-31 v1 Representation Theory
Abstract
Let A(n) be the smooth dual of the p-adic group G=GL(n). We create on A(n) the structure of a complex algebraic variety. There is a morphism of A(n) onto the Bernstein variety Omega G which is injective on each component of A(n). The tempered dual of G is a deformation retract of A(n). The periodic cyclic homology of the Hecke algebra of G is isomorphic to the periodised de Rham cohomology supported on finitely many components of A(n).
Keywords
Cite
@article{arxiv.math/0007107,
title = {Geometry of the smooth dual of GL(n)},
author = {Jacek Brodzki and Roger Plymen},
journal= {arXiv preprint arXiv:math/0007107},
year = {2009}
}
Comments
7 pages, LaTeX