Representation of finite groups: conjectures, reductions, and applications

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Abstract

In this survey, we discuss some basic problems in representation theory of finite groups, including some long-standing conjectures of Alperin, Brauer, and others. A possible approach to some of these problems is to use the classification of finite simple groups to reduce the problem in consideration to some, more specific, questions about simple groups. We will describe recent progress on reduction theorems in this direction. We will also outline applications of these results to various problems in group theory, number theory, and algebraic geometry.

Original languageEnglish (US)
Pages (from-to)87-109
Number of pages23
JournalActa Mathematica Vietnamica
Volume39
Issue number1
DOIs
StatePublished - Mar 1 2014

Keywords

  • Adequate groups
  • Alperin weight conjecture
  • Brauer height zero conjecture
  • Crepant resolutions
  • Finite groups
  • Kollár–Larsen problem
  • Larsen’s conjecture
  • Low-dimensional representations
  • Representation theory
  • Waring problem

ASJC Scopus subject areas

  • Mathematics(all)

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