Exotic symmetric space over a finite field, III

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.