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Separable exterior squares over finite fields

✍ Scribed by Duncan Brydon

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 269 KB
Volume: 268
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00272-2

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✦ Synopsis

The paper concerns exterior squares of polynomials and matrices over the finite field F q for large q. We find the probability that monic f ∈ F q [t] has a non-separable exterior square. We then find the probability that X ∈ GL(d, q) has an exterior square which is non-separable, non-cyclic or nonsemisimple. This should have applications in recognising GL(V ) in its action on V ∧ V , when V is a d-dimensional vector space over F q .

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