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On the geometry and
representation theory of isomeric matrices
Rohit Nagpal, Steven V. Sam and Andrew Snowden |
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Vol. 16 (2022), No. 6, 1501–1529
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Abstract |
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The space of complex matrices can be regarded as an algebraic variety on which the group 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 and vary. We establish analogs of these results for the space of isomeric matrices with respect to the action of , where 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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Keywords
Lie superalgebras, twisted commutative algebras, isomeric
algebra
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Mathematical Subject Classification
Primary: 13A50, 13E05
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Milestones
Received: 2 February 2021
Revised: 21 August 2021
Accepted: 18 September 2021
Published: 27 September 2022
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Authors |
| Rohit Nagpal | |
| Department of Mathematics University of Michigan Ann Arbor, MI United States |
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| Steven V. Sam | |
| Department of Mathematics University of California San Diego, CA United States |
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| Andrew Snowden | |
| Department of Mathematics University of Michigan Ann Arbor, MI United States |
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