Algebra Seminar 

Monday, May 4, 3:30pm-4:20pm, at CW 131 

Speaker: Dr. Yun LIu, Indiana University Bloomington

Title: Cohen–Macaulay Filtrations over Invariant Rings

Abstract: Quasi-invariants of Weyl groups generalize invariant polynomials: although they are usually not polynomial rings, they share interesting features such as freeness over the invariant polynomial ring and therefore Cohen–Macaulay.

In this talk, I will discuss a parallel construction arising from classifying spaces of compact Lie groups. Starting from Borel's identification of $H^*(BG;Q)$ with a ring of Weyl-group invariant polynomials, we construct natural towers of spaces over BG whose rational cohomology rings form descending filtrations between $H^*(BT;Q)$ and $H^*(BG;Q)$. These rings share key algebraic features with quasi-invariants, including freeness over $H^*(BG;Q)$. I will illustrate the construction through examples related to flag manifolds and classifying spaces of commuting elements.