Some homological representations for Grassmannians in cross-characteristics

J Siemons, D Smith

Research output: Contribution to journalArticle


Let F* be the finite field of q elements and let P(n,q) be the projective space of dimension n-1 over F*. We construct a family H^{n}_{k,i} of combinatorial homology modules associated to P(n,q) over a coefficient field F field of characteristic p_{0}>0 co-prime to q. As FGL(n,q)-representations the modules are obtained from the permutation action of GL(n,q) on the subspaces of F*^n. We prove a branching rule for H^{n}_{k,i} and use this rule to determine these homology representations completely. The main results are a duality theorem and the complete characterisation of H^{n}_{k,i} in terms of the standard irreducibles of GL(n,q) over F.
Original languageEnglish
Pages (from-to)157-180
Number of pages24
JournalRussian Academy of Science
Publication statusPublished - 2013

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