A remark on the orthogonality relations for Green functions
Let G be a connected linear algebraic group defined over the finite field \({\mathbb{F}}_ q\) of characteristic p. We denote by k an algebraic closure of \({\mathbb{F}}_ q\) and by F the Frobenius automorphism \((a\mapsto a^ q)\) of k over \({\mathbb{F}}_ q\). Then F operates on G and its group \(G^ F\) of fixed points is the finite group of \({\mathbb{F}}^ q\)-rational points of G. Now assume G to be reductive and let \({\mathcal U}\) be the \({\mathbb{F}}_ q\)- variety of unipotent elements of G. The Green functions of \(G^ F\) are class functions \(Q_{T,G}\) defined on the set \({\mathcal U}^ F\) of unipotent elements of \(G^ F\), parametrized by a maximal torus T of G defined over \({\mathbb{F}}_ q\) (and depending only on the \(G^ F\)-conjugacy class of T). They are of importance for the representation theory of \(G^ F\).
scientific article; zbMATH DE number 4071210
scientific article