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Root-free exterior squares over finite fields

✍ Scribed by Duncan Brydon

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 178 KB
Volume: 262
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(02)00664-6

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✦ Synopsis

The paper is devoted to exterior squares of polynomials and matrices over the finite field F q for large q. We find the limit as d → ∞ of the probability that a monic polynomial f ∈ F q [t] of degree d has root-free exterior square. We also find the limit as d → ∞ of the probability that a matrix X ∈ GL(d, q) has eigenvalue-free exterior square. This should be useful 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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