Eisenstein Series on Loop Groups

Details Eisenstein Series on Loop Groups Eisenstein Series on Loop Groups

2011-03-22

arxiv.org/abs/1103.4212v1

Mathematics

Representation Theory

Scientific paper

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.

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