Hartley´s Theorem on Representations of the General Linear Groups and Classical Groups

Authors : A. E. ZALESSKI

Pages : 211-225

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :We suggest a new proof of Hartley`s theorem on representations of the general linear groups GLninsert ignore into journalissuearticles values(K); where K is a field. Let H be a subgroup of GLninsert ignore into journalissuearticles values(K); and E the natural GLninsert ignore into journalissuearticles values(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 GLninsert ignore into journalissuearticles values(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