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Lie Groups pp 427-435 | Cite as

Unitary Branching Rules and Tableaux

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

Abstract

In this chapter, representations of both \(\mathrm{GL}(n, \mathbb{C})\) and \(\mathrm{GL}(n - 1, \mathbb{C})\) occur. To distinguish the two, we will modify the notation introduced before Theorem 36.3 as follows. If λ is a partition (of any k) of length \( \leqslant \) n, or more generally an integer sequence \(\lambda = (\lambda _{1}, \ldots, \lambda _{n})\) with \(\lambda _{1} \geqslant\lambda _{2} \geqslant\cdots \), we will denote by \(\pi _{\lambda }^{\mathrm{GL}_{n}}\) or more simply as π λ the representation of \(\mathrm{GL}(n, \mathbb{C})\) parametrized by λ. On the other hand, if μ is a partition of length \( \leqslant \) n − 1, or more generally an integer sequence μ = (μ 1,,μ n−1) with \(\mu _{1} \geqslant\mu _{2} \geqslant\cdots \), we will denote by \(\pi _{\mu }^{\mathrm{GL}_{n-1}}\) or (more simply) as π μ ′ the representation of \(\mathrm{GL}(n - 1, \mathbb{C})\) parametrized by μ.

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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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