Modular Representations of Finite Groups of Lie Type

The first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic. Ordinary and modular representations are explored in the context of Deligne–Lusztig characters. This treatment is accessible to researchers in neighbouring parts of group theory, number theory, and topology.

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Finite groups of Lie type encompass most of the finite simple groups. Their representations and characters have been studied intensively for half a century, though some key problems remain unsolved. This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic. As a subtheme, the relationship between ordinary and modular representations is explored, in the context of Deligne–Lusztig characters. One goal has been to make the subject more accessible to those working in neighbouring parts of group theory, number theory, and topology. Core material is treated in detail, but the later chapters emphasize informal exposition accompanied by examples and precise references.