On the cohomology of line bundles over certain flag schemes II

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:178

Article

Liu, Linyuan¹  Polo, Patrick¹ 

[1] Sorbonne Univ, Inst Math Jussieu Paris Rive Gauche, Campus Pierre & Marie Curie,4 Pl Jussieu, F-75252 Paris 05, France

关键词: Cohomology;    Line bundles;    Flag schemes;    Weyl modules;    Symmetric functions;   

DOI  :  10.1016/j.jcta.2020.105352

来源: Elsevier

【 摘 要 】

Over a field K of characteristic p, let Z be the incidence variety in P-d x (P-d)* and let L be the restriction to Z of the line bundle O(-n - d) boxed times O(n), where n = p + f with 0 <= f <= p -2. We prove that H-d (Z, L) is the simple GL(d+1)-module corresponding to the partition lambda(f) = (p - 1 f, p - 1, f + 1). When f = 0, using the first author's description of H-d(Z, L) and Jantzen's sum formula, we obtain as a byproduct that the sum of the monomial symmetric functions m(lambda), for all partitions lambda of 2p - 1 less than (p - 1, p - 1, 1) in the dominance order, is the alternating sum of the Schur functions S-p-1,S-p-1-i,S-1i+1 for i = 0, ..., p - 2. (C) 2020 Published by Elsevier Inc.

【 授权许可】

Free