- Turkish Journal of Mathematics
- Vol: 31 Issue: Suppl
- Hartley´s Theorem on Representations of the General Linear Groups and Classical Groups
Hartley´s Theorem on Representations of the General Linear Groups and Classical Groups
Authors : A. E. Zalesski
Pages : 211-225
View : 9 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :We suggest a new proof of Hartley's theorem on representations of the general linear groups GLn(K) where K is a field. Let H be a subgroup of GLn(K) and E the natural GLn(K)-module. Suppose that the restriction E|H of E to H contains a regular KH-module. The theorem asserts that this is then true for an arbitrary GLn(K)-module M provided dim M>1 and H is not of exponent 2. Our proof is based on the general facts of representation theory of algebraic groups. In addition, we provide partial generalizations of Hartley's theorem to other classical groups.Keywords : subgroups of classical groups, representation theory of algebraic groups