On an asymptotic behavior of elements of order p in irreducible representations of the classical algebraic groups with large enough highest weights

2000/03/31 by I. D. Suprunenko
Mathematics · #math.RT #msc:20G05

paper · pdf

published as Proc. Amer. Math. Soc. 129 (2001) 2581-2589 · 8 pages, LaTeX2e. See also http://im.bas-net.by/~suprunenko/papers Revision. An inaccuracy in the estimate for groups of type B is corrected. The result has not changed in an asymptotical sense

arxiv created 2002/05/15 · arxiv updated 2009/11/30

Abstract

The behavior of the images of a fixed element of order p in irreducible representations of a classical algebraic group in odd characteristic p with highest weights large enough with respect to p and this element is investigated. Lower estimates for the number of Jordan blocks of size p in images of such elements that lie in naturally embedded subgroups of the same type as the initial group and smaller ranks are obtained.

Related

• Irreducible representations of simple algebraic groups in which a\n unipotent element is represented by a matrix with single non-trivial Jordan\n block
• Character values at elements of order 2
• Rank and Duality in Representation Theory
• Principal blocks, irreducible restriction, fields and degrees
• Low-dimensional irreducible rational representations of classical algebraic groups