Vaibhav Pandey : Are natural embeddings of determinantal rings split?

Posted by Wenliang Zhang , part of the Commutative Algebra Seminar.

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Feb. 9, 2022, 3 p.m.

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Abstract

Over an infinite field, a generic determinantal ring is the fixed subring of an action of the general linear group on a polynomial ring; this is the natural embedding of the title. If the field has characteristic zero, the general linear group is linearly reductive, and it follows that the invariant ring is a split subring of the polynomial ring. We determine if the natural embedding is split in the case of a field of positive characteristic. Time permitting, we will address the corresponding question for Pfaffian and symmetric determinantal rings. This is ongoing work with Mel Hochster, Jack Jeffries, and Anurag Singh.