An extension of the method of Iwahori algebra (Q1109141)

The present paper examines three different types of induced representations for algebraic groups over algebraically closed fields K. The method of Hecke algebras (or Iwahori algebras) of finite Chevalley groups (over Z) is extended to the case of Chevalley groups G over K. In the case of finite groups, all three kinds of inductions are the same. Two of the three induction processes make sense in general (one of them is sometimes called ''co-induction'' because of its connection with cohomology theory by way of Shapiro's Lemma). The third induction process is based on character theory so that it would only make sense when applied to a finite dimensional representation of a subgroup. The reviewer finds the notation a bit difficult to follow. For example, Definition 1.7 does not appear to be consistent with the definition given in the introduction in the case of a 1-dimensional representation \(V\).