Exotic symmetric space over a finite field, III

TL;DR

This paper provides a conceptual framework for character sheaves on exotic symmetric spaces over finite fields, establishing their classification and connecting explicit constructions with a Ginzburg-inspired approach.

Contribution

It introduces a Ginzburg type conceptual definition of character sheaves on exotic symmetric spaces and proves their equivalence to previous explicit constructions.

Findings

Ginzburg type character sheaves coincide with explicit constructions

Classification of Ginzburg type character sheaves achieved

Provides a conceptual understanding of character sheaves on X

Abstract

Let X be an exotic symmetric space G/H \times V, where G= GL(V) and H = Sp(V) for a symplectic vector space V over an algebraically closed field of odd characteristic. In our previous papers, character sheaves on X were constructed based on the explicit data. In this paper, we give a conceptual definition of character sheaves on X based on the idea of Ginzburg in the case of symmetric spaces, which we call Ginzburg type character sheaves. We prove that Ginzburg type character sheaves on X actually coincide with those defined in our papers. This gives a classification of Ginzburg type character sheaves on X.