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Lie Groups pp 445-454 | Cite as

The Involution Model for Sk

  • Daniel Bump
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)

Abstract

Let σ 1 = 1, σ 2 = (12), σ 3 = (12)(34), be the conjugacy classes of involutions in S k . It was shown by Klyachko and by Inglis et al. [82] that it is possible to specify a set of characters \(\psi _{1},\psi _{2},\psi _{3},\ldots\) of degree 1 of the centralizers of \(\sigma _{1},\sigma _{2},\sigma _{3},\ldots\) such that the direct sum of the induced representations of the \(\psi_i\) contains every irreducible representation exactly once. In the next chapter, we will see that translating this fact and related ones to the unitary group gives classical facts about symmetric and exterior algebra decompositions due to Littlewood [120].

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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