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Lie Groups pp 427-435

# 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