SEMINAR: Groups and Combinatorics Seminar:Primary Cyclic Matrices


Groups and Combinatorics Seminar
Brian Corr (UWA)
will speak on
Primary Cyclic Matrices
at 1pm Tuesday 7 September in MLR2
Abstract: Let G be an algebra of dxd matrices over a field F and denote m_X(t) and c_X(t) the minimal and the characteristic polynomials of X in G. X in called fprimary cyclic if f is a monic irreducible divisor if m_X(t) does not divide the quotient c_X(t)/m_X(t), and simply primary cyclic if it is fprimary cyclic for some f.
In 2006, Glasby described a version of the MEATAXE test for irreducibility which makes use of primary cyclic matrices, and in 2008 Glasby and Praeger determined the proportion of primary cyclic matrices in the full matrix algebra M(d,q). We use methods of generating functions and the Cycle Index Theorem to produce a lower bound for the proportion of primary cyclic matrices in the irreducible subalgebra M(c,q^b), and describe some asymptotic behaviour.
All welcome
Speaker(s) 
Brian Corr

Location 
Maths Lecture Room 2


Contact 
Michael Giudici
<[email protected]>

Start 
Tue, 07 Sep 2010 13:00

End 
Tue, 07 Sep 2010 13:45

Submitted by 
Michael Giudici <[email protected]>

Last Updated 
Mon, 06 Sep 2010 15:07

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