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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 211A: Seminar in Algebra
Dr. Karthik Ganapathy
UCSD
Weyl's polarization theorem in positive characteristic
Abstract:
Given a representation $W$ of a group $G$, polarization is a technique to obtain polynomial invariants for the diagonal action of $G$ on $W^{\oplus r+1}$ from invariants of $W^{\oplus r}$. Weyl's theorem on polarization tells us when one can obtain all polynomial invariants of $W^{\oplus r+1}$ via this process. I will survey some results on polarization in the positive characteristic setting from the last three decades and explain how this can be used to obtain negative answers to some noetherian problems in infinite-dimensional/noncommutative algebra.
March 3, 2025
3:00 PM
APM 7321
Research Areas
Algebra****************************
