SPRINGER’S THEOREM FOR MODULAR COINVARIANTS OF GLn(Fq)
نویسنده
چکیده
Two related results are proven in the modular invariant theory of GLn(Fq ). The first is a finite field analogue of a result of Springer on coinvariants of the symmetric group Sn acting on C[x1, . . . , xn]. It asserts that the following two Fqn [GLn(Fq )×F × q ]modules have the same composition factors: • the coinvariant algebra for GLn(Fq ) acting on Fqn [x1, . . . , xn], in which GLn(Fq ) acts as a subgroup of GLn(Fqn) by linear substitutions of variables, and F×qn acts by scalar substitutions of variables, • the action on the group algebra Fqn [GLn(Fq )] by left and right multiplication. The second result is a related statement about parabolic invariants and coinvariants.
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