Graduate Algebra Symposium

Chelsea Drescher

Invariants of GL(n,q) in Polynomial and Quotient Rings

In this talk, we will consider the action of GL(n,q), where q is a prime power, on the polynomials in n indeterminates with coefficients from the finite field of order q. We will briefly review the Dickson subalgebra of invariants and its Hilbert Series. Then we will define a Frobenius power of the ideal generated by the n indeterminates and consider the quotient of the polynomial ring by this ideal. Using examples, we will examine the invariants in the quotient space under the descended action and we will consider a conjecture made by J. Lewis, V. Reiner, and D. Stanton.