On the cohomology of line bundles over certain flag schemes

DOI10.1016/J.JCTA.2021.105448arXiv1908.08438MaRDI QIDQ6324043

Linyuan Liu

Publication date: 22 August 2019

Abstract: Let $G$ be the group scheme $operatorname{SL}_{d+1}$ over $mathbbZ$ and let $Q$ be the parabolic subgroup scheme corresponding to the simple roots $alph{a}_2,cdots,alph{a}_{d-1}$. Then $G/Q$ is the $mathbbZ$-scheme of partial flags $D_{1}subset{H}_{d}subsetV$. We will calculate the cohomology modules of line bundles over this flag scheme. We will prove that the only non-trivial ones are isomorphic to the kernel or the cokernel of certain matrices with multinomial coefficients.

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Grassmannians, Schubert varieties, flag manifolds (14M15) Combinatorial aspects of algebraic geometry (05E14)

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