Schur-Weyl Duality and the Relationship Between Representations of Sd and GLn (ℂ)

Lakshmibai, V.; Brown, Justin

doi:10.1007/978-981-13-1393-6_6

V. Lakshmibai³ &
Justin Brown⁴

Part of the book series: Texts and Readings in Mathematics ((TRIM,volume 53))

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Abstract

In this chapter, we discuss the representation theory of GL_n (ℂ). Schur modules are introduced and are shown to be irreducible GL_n (ℂ)-modules, using Schur-Weyl duality. We then discuss the representation theory of SL_n(ℂ), and deduce the representation theory of GL_n (ℂ). For further details, refer to [23].

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Northeastern University, Boston, MA, USA
V. Lakshmibai
Olivet Nazarene University, Bourbonnais, IL, USA
Justin Brown

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V. Lakshmibai
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Justin Brown
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Correspondence to V. Lakshmibai .

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Lakshmibai, V., Brown, J. (2018). Schur-Weyl Duality and the Relationship Between Representations of S_d and GL_n (ℂ). In: Flag Varieties. Texts and Readings in Mathematics, vol 53. Springer, Singapore. https://doi.org/10.1007/978-981-13-1393-6_6

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DOI: https://doi.org/10.1007/978-981-13-1393-6_6
Publisher Name: Springer, Singapore
Online ISBN: 978-981-13-1393-6
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