Some homological representations for Grassmannians in cross-characteristics

Siemons, J and Smith, D (2013) Some homological representations for Grassmannians in cross-characteristics. Russian Academy of Science, 414. pp. 157-180.

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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.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Users 2731 not found.
Date Deposited: 11 Jan 2012 14:21
Last Modified: 18 Feb 2021 00:43

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