Spherical varieties and integral representations of L-functions
Abstract
We present a conceptual and uniform interpretation of the methods of integral representations of L-functions (period integrals, Rankin-Selberg integrals). This leads to: (i) a way to classify of such integrals, based on the classification of certain embeddings of spherical varieties (whenever the latter is available), (ii) a conjecture which would imply a vast generalization of the method, and (iii) an explanation of the phenomenon of "weight factors" in a relative trace formula. We also prove results of independent interest, such as the generalized Cartan decomposition for spherical varieties of split groups over p-adic fields (following an argument of Gaitsgory and Nadler).
Cite
@article{arxiv.0905.4245,
title = {Spherical varieties and integral representations of L-functions},
author = {Yiannis Sakellaridis},
journal= {arXiv preprint arXiv:0905.4245},
year = {2013}
}
Comments
Appeared in Algebra & Number Theory, Vol. 6 (2012), No. 4, 611-667. Formula for subgroup H after example 4.5.1 missing from published version