Modular invariants for some finite modular pseudo-reflection groups

In this paper, we determine the modular invariants for some pseudo-reflection subgroups of the finite general linear group GLn(q) acting on the tensor product of the symmetric algebra S center dot(V) and the exterior algebra perpendicular to center dot(V) of the natural GLn(q)-module V. We are particularly interested in the case when the pseudo-reflection groups are subgroups of the parabolic subgroup of GLn(q) which are generalization of Weyl groups of Cartan type Lie algebra.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

In this paper, the modular invariants for certain pseudo-reflection subgroups of the finite general linear group GLn(q) acting on the tensor product of the symmetric algebra S center dot(V) and the exterior algebra perpendicular to center dot(V) of the natural GLn(q)-module V are determined. The focus is on the case when the pseudo-reflection groups are subgroups of the parabolic subgroup of GLn(q) which are generalizations of Weyl groups of Cartan type Lie algebra.