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Representations of\({\mathfrak{U}_d}\)and\(G{L_2}\left( {{\mathbb{F}_q}} \right)\)

  • William Fulton
  • Joe Harris
Part of the Graduate Texts in Mathematics book series (GTM, volume 129)

Abstract

In this lecture we analyze the representation of two more types of groups: the alternating groups\({\mathfrak{U}_d}\)and the linear groups \(G{L_2}\left( {{\mathbb{F}_q}} \right)\) and \(S{L_2}\left( {{\mathbb{F}_q}} \right) \) over finite fields. In the former case, we prove some general results relating the representations of a group to the representations of a subgroup of index two, and use what we know about the symmetric group; this should be completely straightforward given just the basic ideas of the preceding lecture. In the latter case we start essentially from scratch. The two sections can be read (or not) independently; neither is logically necessary for the remainder of the book.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • William Fulton
    • 1
  • Joe Harris
    • 2
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA

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