Eisenstein Series on Loop Groups
Representation Theory
2015-05-07 v2
Abstract
Based on Garland's work, in this paper we construct the Eisenstein series on the adelic loop groups over a number field, induced from either a cusp form or a quasi-character which is assumed to be unramified. We compute the constant terms, prove their absolute and uniform convergence under the affine analog of Godement's criterion. For the case of quasi-characters the resulting formula is an affine Gindikin-Karpelevich formula. Then we prove the convergence of Eisenstein series themselves in certain analogs of Siegel subsets.
Cite
@article{arxiv.1103.4212,
title = {Eisenstein Series on Loop Groups},
author = {Dongwen Liu},
journal= {arXiv preprint arXiv:1103.4212},
year = {2015}
}
Comments
To appear in Transactions of the AMS