Cusp Eigenforms and the Hall Algebra of an Elliptic Curve
Representation Theory
2019-02-20 v1 Algebraic Geometry
Number Theory
Abstract
We give an explicit construction of the cusp eigenforms on an elliptic curve defined over a finite field using the theory of Hall algebras and the Langlands correspondence for function fields and . As a consequence we obtain a description of the Hall algebra of an elliptic curve as an infinite tensor product of simpler algebras. We prove that all these algebras are specializations of a universal spherical Hall algebra (as defined and studied in \cite{BS} and \cite{SV1}).
Keywords
Cite
@article{arxiv.1109.4308,
title = {Cusp Eigenforms and the Hall Algebra of an Elliptic Curve},
author = {Dragos Fratila},
journal= {arXiv preprint arXiv:1109.4308},
year = {2019}
}