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

## Abstract

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 |
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Faculty \ School: | Faculty of Science > School of Mathematics |

UEA Research Groups: | Faculty of Science > Research Groups > Algebra and Combinatorics |

Depositing User: | Users 2731 not found. |

Date Deposited: | 11 Jan 2012 14:21 |

Last Modified: | 15 Jun 2023 11:07 |

URI: | https://ueaeprints.uea.ac.uk/id/eprint/36099 |

DOI: |

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