Invariants of Landweber-Stong reflection groups modulo Frobenius powers
UNT Graduate Algebra Group
Speaker: Chelsea DrescherDate: September 3, 2019
Location: GAB 439A
Abstract: Lewis, Reiner, and Stanton conjectured a combinatorial description for the Hilbert series of invariants in the polynomial ring modulo Frobenius powers under the action of the general linear group over arbitrary finite fields. We will solve a local case of the conjecture by considering subgroups of the general linear group that fix one hyperplane. When the characteristic of the underlying field divides the order of the group, the subgroup fixing a reflecting hyperplane is a semi-direct product of diagonalizable reflections and transvections. We will provide an explicit description of the invariant ring for these Landweber-Stong groups reflecting about a fixed hyperplane. In addition, we will show that the Hilbert series of the invariant space counts orbits, solving a special case of the Lewis-Reiner-Stanton conjecture.
Fall 2019 Schedule
September 3 | Invariants of Landweber-Stong reflection groups modulo Frobenius powers | Chelsea Drescher |
September 17 | Group theory qual practice | Thomas Calkin |
September 24 | Introduction to deformation theory | Naomi Krawzik |
October 8 | Classification of graded Hecke algebras | Naomi Krawzik |
October 15 | Classification of graded Hecke algebras | Naomi Krawzik |
October 22 | Group theory qual practice | Dillon Hanson, Naomi Krawzik, Colin Lawson |
October 29 | Invariant differential forms | Dillon Hanson |
November 5 | An introduction to Hochshild cohomology and deformations | Colin Lawson |
November 26 | Sums of three squares along arithmetic progressions | Ethan Malmer |
- Return to Dillon Hanson's home page.