A motivated introduction to character sheaves and the orbit method for unipotent groups in positive characteristic

Details A motivated introduction to character sheaves and the orbit method for unipotent groups in positive characteristic A motivated introduction to character sheaves and the orbit method for unipotent groups in positive characteristic

2006-09-27

arxiv.org/abs/math/0609769v2

Mathematics

Representation Theory

77 pages, LaTeX. A few proofs are missing from this version of the paper (only the essential ideas are sketched), but otherwis

Scientific paper

This article is based on lectures given by the authors in 2005 and 2006. Our first goal is to present an introduction to the orbit method with an emphasis on the character theory of finite nilpotent groups. The second goal (motivated by a recent work of G. Lusztig) is to explain several nontrivial aspects of character theory for finite groups of the form $G(F_{q^n})$, where $G$ is a unipotent algebraic group over a finite field $F_q$. In particular, we introduce the notion of a character sheaf for a unipotent group, and provide a toy model for the representation-theoretic notion of an L-packet.

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