2024/12/30 by Steven V Sam, Sam, Steven V, Andrew Snowden +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2412.20797
openalex publication_date 2024/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.