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Conjugacy classes in unitriangular matrices

✍ Scribed by Antonio Vera-López; J.M. Arregi

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
290 KB
Volume
370
Category
Article
ISSN
0024-3795

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Let n = n q be the group of the upper unitriangular matrices of size n over q , the finite field of q = p t elements. G. Higman has conjectured that, for each n, the number of conjugacy classes of elements of n is a polynomial expression in q. In this paper we prove that the number of conjugacy clas

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A general conjecture is given for an explicit basis of the coordinate ring of the closure of the conjugacy class of a nilpotent matrix. This conjecture is proven when the partition given by the transpose Jordan type of the nilpotent matrix is a hook or has two parts.