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2022 On the geometry and representation theory of isomeric matrices
Rohit Nagpal, Steven V. Sam, Andrew Snowden
Algebra Number Theory 16(6): 1501-1529 (2022). DOI: 10.2140/ant.2022.16.1501

Abstract

The space of n×m complex matrices can be regarded as an algebraic variety on which the group GLn×GLm acts. There is a rich interaction between geometry and representation theory in this example. In an important paper, de Concini, Eisenbud, and Procesi classified the equivariant ideals in the coordinate ring. More recently, we proved a noetherian result for families of equivariant modules as n and m vary. We establish analogs of these results for the space of (n|n)×(m|m) isomeric matrices with respect to the action of Qn×Qm, where Qn is the automorphism group of the isomeric structure (commonly known as the “queer supergroup”). Our work is motivated by connections to the Brauer category and the theory of twisted commutative algebras.

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Rohit Nagpal. Steven V. Sam. Andrew Snowden. "On the geometry and representation theory of isomeric matrices." Algebra Number Theory 16 (6) 1501 - 1529, 2022. https://doi.org/10.2140/ant.2022.16.1501

Information

Received: 2 February 2021; Revised: 21 August 2021; Accepted: 18 September 2021; Published: 2022
First available in Project Euclid: 2 October 2022

Digital Object Identifier: 10.2140/ant.2022.16.1501

Subjects:
Primary: 13A50 , 13E05

Keywords: isomeric algebra , Lie superalgebras , twisted commutative algebras

Rights: Copyright © 2022 Mathematical Sciences Publishers

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Vol.16 • No. 6 • 2022
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