On the excursion algebra
Dennis Gaitsgory, Kevin Lin, Wyatt Reeves
TL;DR
This paper studies the excursion algebra linked to schemes over finite fields and reductive groups, exploring its properties and its action on automorphic functions when X is a curve.
Contribution
It establishes fundamental properties of the excursion algebra associated with schemes over finite fields and reductive groups, especially its action on automorphic functions.
Findings
Basic properties of the excursion algebra are established.
The algebra acts on automorphic functions when X is a curve.
Framework connects algebraic structures to automorphic forms.
Abstract
The excursion algebra associated to a scheme X over a finite field and a reductive group G is the algebra of global functions on the stack of arithmetic G-local systems on X. When X is a curve, this algebra acts on the space of automorphic functions. In this paper we establish some basic properties of this algebra.
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models