Let G be a finite group, and V a finite-dimensional semisimple G-module over a finite field. Assume that V is endowed with a nonsingular bilinear form which is symmetric or symplectic, and which is invariant under the action of G. In this setting, we compute the number of anisotropic simple submodules of V.
On the number of anisotropic simple submodules in modules with a form / E. Pacifici. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - 84:1(2005), pp. 1-10.
On the number of anisotropic simple submodules in modules with a form
E. PacificiPrimo
2005
Abstract
Let G be a finite group, and V a finite-dimensional semisimple G-module over a finite field. Assume that V is endowed with a nonsingular bilinear form which is symmetric or symplectic, and which is invariant under the action of G. In this setting, we compute the number of anisotropic simple submodules of V.
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