On a strange invariant bilinear form on the space of automorphic forms
Number Theory
2016-10-06 v4 Algebraic Geometry
Representation Theory
Abstract
Let F be a global field and A its ring of adeles. Let G:=SL(2). We study the bilinear form B on the space of K-finite smooth compactly supported functions on G(A )/G(F) defined by the formula B (f,g):=B'(f,g)-(M^{-1}CT (f),CT (g)), where B' is the usual scalar product, CT is the constant term operator, and M is the standard intertwiner. This form is natural from the viewpoint of the geometric Langlands program. To justify this claim, we provide a dictionary between the classical and "geometric" theory of automorphic forms. We also show that the form B is related to S. Schieder's Picard-Lefschetz oscillators.
Keywords
Cite
@article{arxiv.1503.04705,
title = {On a strange invariant bilinear form on the space of automorphic forms},
author = {Vladimir Drinfeld and Jonathan Wang},
journal= {arXiv preprint arXiv:1503.04705},
year = {2016}
}
Comments
Typos corrected