The SL(2)-type and Base Change
Number Theory
2008-08-27 v1 Representation Theory
Abstract
The SL(2)-type of any smooth, irreducible and unitarizable representation of GL(n) over a p-adic field was defined by Venkatesh. We provide a natural way to extend the definition to all smooth and irreducible representations. For unitarizable representations we show that the SL(2)-type of a representation is preserved under base change with respect to any finite extension. The Klyachko model of a smooth, irreducible and unitarizable representation \pi of GL(n) depends only on the SL(2)-type of \pi. As a consequence we observe that the Klyachko model of \pi and of its base-change are of the same type.
Keywords
Cite
@article{arxiv.0808.3405,
title = {The SL(2)-type and Base Change},
author = {Omer Offen and Eitan Sayag},
journal= {arXiv preprint arXiv:0808.3405},
year = {2008}
}
Comments
10 pages