Abstract
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)⊠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 λf=(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.
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