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On the p-rank of finite Hermitian unitals
by
Robert A. Liebler
Colorado State University
In 1979 Andriamanalimanana conjectured a formula for p-rank r of these unitals when p | q+1. This formula has attracted substantial interest because it would settle one of the last open questions concerning the modular irreducible representations of finite groups of Lie type. I will show how to ``encrypt'' the Hermitian unital as a 2 by 2 matrix over a certain group ring, to eventually produce a formula for r. This formula requires the computation of the p-rank, a, of a certain q by q matrix and has allowed verification of the conjecture for q <= 26. In case both p and q are odd, I will show how to ``decrypt'' the Hermitian unital as a configuration of planar ovals in PG(3, q). The collinearity graph of the generalized quadrangle W(q) leads to a new lower bound on a and therefore r.
Date received: March 12, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagg-21.