The paper derives explicit Hilbert series and dimension formulas for invariants of hyperplane pointwise stabilizers in GL_n(F_q) acting on polynomials modulo Frobenius powers, a local case of the Lewis-Reiner-Stanton conjecture.
Gordon, On the quotient ring by diagonal invariants , Invent
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Invariants of polynomials mod Frobenius powers
The paper derives explicit Hilbert series and dimension formulas for invariants of hyperplane pointwise stabilizers in GL_n(F_q) acting on polynomials modulo Frobenius powers, a local case of the Lewis-Reiner-Stanton conjecture.