Modular invariants under the actions of some reflection groups related to Weyl groups
Bull. Korean Math. Soc.
Published online August 2, 2019
Kenshi Ishiguro, Takahiro Koba, Toshiyuki Miyauchi, and Erika Takigawa
Fukuoka University, Wakaba senior high school
Abstract : Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group is expressed as the ring of invariants, which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the symplectic groups. We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space.
Keywords : invariant theory, unstable algebra, pseudo--reflection group, Poincar\'e series, Lie group, $p$--compact group, classifying space
MSC numbers : 55R35
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