no. 3
Cohomology of flag supervarieties and resolutions of determinantal ideals. II
Sam, Steven V1 orcid ; Snowden, Andrew Wilson2 orcid
1Department of Mathematics, University of California, San Diego, CA
2Department of Mathematics, University of Michigan, Ann Arbor, MI
Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 457-485

We compute the coherent cohomology of the structure sheaf of complex periplectic Grassmannians. In particular, we show that it can be decomposed as a tensor product of the singular cohomology ring of a Grassmannian for either the symplectic or orthogonal group together with a semisimple representation of the periplectic Lie supergroup. The restriction of the latter to its even subgroup has an explicit multiplicity-free description in terms of Schur functors and is closely related to syzygies of (skew-)symmetric determinantal ideals. We develop tools for studying splitting rings for Coxeter groups of types BC and D, which may be of independent interest.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/art.47
Classification: 14M30
Keywords: supergeometry, Grassmannian, syzygies

Sam, Steven V  1 ; Snowden, Andrew Wilson  2

1 Department of Mathematics, University of California, San Diego, CA
2 Department of Mathematics, University of Michigan, Ann Arbor, MI
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Sam, Steven V; Snowden, Andrew Wilson. Cohomology of flag supervarieties and resolutions of determinantal ideals. II. Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 457-485. doi: 10.5802/art.47
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