Cusp Eigenforms and the Hall Algebra of an Elliptic Curve

Details Cusp Eigenforms and the Hall Algebra of an Elliptic Curve Cusp Eigenforms and the Hall Algebra of an Elliptic Curve

2011-09-20

arxiv.org/abs/1109.4308v1

Mathematics

Representation Theory

Scientific paper

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 $\GL_n$. 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}).

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