On the characteristic map of finite unitary groups

Details On the characteristic map of finite unitary groups On the characteristic map of finite unitary groups

2005-11-09

arxiv.org/abs/math/0511220v1

Mathematics

Representation Theory

Scientific paper

In his classic book on symmetric functions, Macdonald describes a remarkable result by Green relating the character theory of the finite general linear group to transition matrices between bases of symmetric functions. This connection allows us to analyze the representation theory of the general linear group via symmetric group combinatorics. Using the work of Ennola, Kawanaka, Lusztig and Srinivasan, this paper describes the analogous setting for the finite unitary group. In particular, we explain the connection between Deligne-Lusztig theory and Ennola's efforts to generalize Green's work, and deduce various representation theoretic results from these results. Applications include finding certain sums of character degrees, and a model of Deligne-Lusztig type for the finite unitary group, which parallels results of Klyachko and Inglis and Saxl for the finite general linear group.

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