2019/08/22 by Linyuan Liu, Liu, Linyuan, Patrick Polo +1 · 1 citation
Mathematics · #05E05 #05E10 #14L15 #20G05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1908.08432
openalex publication_date 2019/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Over a field K of characteristic p, let Z be the incidence variety in ℙd × (ℙd)^* and let L be the restriction to Z of the line bundle O(-n-d) \boxtimes O(n), where n = p+f with 0 ≤ f ≤ p-2. We prove that Hd(Z,L) is the simple GLd+1-module corresponding to the partition λ0 = (p-1+f,p-1,f+1). When f= 0, using the first author's description of Hd(Z,L) and Jantzen's sum formula, we obtain as a by-product that the sum of the monomial symmetric functions mλ, for all partitions λ of 2p-1 less than (p-1,p-1,1) in the dominance order, is the alternating sum of the Schur functions Sp-1,p-1-i,1i+1 for i=0,…,p-2.