On the cohomology of line bundles over certain flag schemes

被引：2

作者：

Liu, Linyuan ^{[1
]}

机构：

[1] Sorbonne Univ, Inst Math Jussieu Paris Rive Gauche, Campus Pierre & Marie Curie, F-75252 Paris 05, France

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2021年 / 182卷

关键词：

Cohomology; Line bundles; Flag schemes; Weyl modules; Multinomial coefficients;

D O I：

10.1016/j.jcta.2021.105448

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be the group scheme SLd+1 over Z and let Q be the parabolic subgroup scheme corresponding to the simple roots alpha(2), ..., alpha(d-1). Then G/Q is the Z-scheme of partial flags {D-1 subset of H-d subset of V}. 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. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：25

共 9 条

[1]

[Anonymous], 1993, Algebraic Varieties

[2] THE SUBMODULE STRUCTURE OF CERTAIN WEYL MODULES FOR GROUPS OF TYPE-AN [J].