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Bivectors over a Finite Field

Published online by Cambridge University Press:  20 November 2018

J. A. MacDougall
J. A. MacDougall*
Affiliation:
University of P.E.I., Charlottetown, P.E.I., Canada, CIA 4P3
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Abstract

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Let U be an n -dimensional vector space over a finite field of q elements. The number of elements of Λ2U of each irreducible length is found using the isomorphism of Λ2U with Hn, the space of n x n skew-symmetric matrices, and results due to Carlitz and MacWilliams on the number of skew-symmetric matrices of any given rank.

Keywords

15A75Grassmann SpacesExterior powers
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 4 , 01 December 1981 , pp. 489 - 490
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Carlitz, L., Representations by Skew Forms in a Finite Field, Arch. Math. V, 1954, p. 19-31.Google Scholar
2. MacWilliams, J., Orthogonal Matrices over Finite Fields, Amer. Math. Monthl. 76 (1969), 152-164.Google Scholar
3. Marcus, M. and Westwick, R., Linear Maps on Skew-Symmetric Matrices: The Invariance of the Elementary Symmetric Functions, Pac. Jour. Math. 10 (1960), 917-924.Google Scholar