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Representations of finite reductive groups: from characteristic zero to transverse characteristic

Introductory Workshop: Group Representation Theory and Applications February 05, 2018 - February 09, 2018

February 09, 2018 (11:00 AM PST - 12:00 PM PST)
Speaker(s): Olivier Dudas (Université de Paris VII (Denis Diderot))
Location: MSRI: Simons Auditorium
  • Decomposition numbers

  • Finite groups of Lie type

  • finite reductive groups

  • basic sets

  • Deligne-Lusztig theory

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



This series of lectures will be centered on decomposition numbers for a special class of finite groups such as GL_n(q), SO_n(q),... E_8(q). I will first present what kind of numerical invariants decomposition numbers are, and what representation-theoretic problems they can solve. For finite reductive groups, I will explain how one can use Deligne--Lusztig theory to get basic sets of ordinary characters and to compute decomposition numbers. If time permits, I will mention a few open problems, including the case of small characteristic.


Lecture 1 - Generalities on decomposition numbers

Lecture 2 - Basic sets for finite reductive groups

Lecture 3 - Computing decomposition numbers

Supplements No Notes/Supplements Uploaded
Video/Audio Files


H.264 Video 16-Dudas.mp4 230 MB video/mp4 rtsp://videos.msri.org/data/000/030/585/original/16-Dudas.mp4 Download
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