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2018 On the minuscule representation of type $B_n$
William J. Cook, Noah A. Hughes
Involve 11(5): 721-733 (2018). DOI: 10.2140/involve.2018.11.721

Abstract

We study the action of the Weyl group of type Bn acting as permutations on the set of weights of the minuscule representation of type Bn (also known as the spin representation). Motivated by a previous work, we seek to determine when cycle structures alone reveal the irreducibility of these minuscule representations. After deriving formulas for the simple reflections viewed as permutations, we perform a series of computer-aided calculations in GAP. We are then able to establish that, for certain ranks, the irreducibility of the minuscule representation cannot be detected by cycle structures alone.

Citation

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William J. Cook. Noah A. Hughes. "On the minuscule representation of type $B_n$." Involve 11 (5) 721 - 733, 2018. https://doi.org/10.2140/involve.2018.11.721

Information

Received: 23 April 2014; Revised: 6 November 2017; Accepted: 20 November 2017; Published: 2018
First available in Project Euclid: 12 April 2018

zbMATH: 06866579
MathSciNet: MR3784022
Digital Object Identifier: 10.2140/involve.2018.11.721

Subjects:
Primary: 17B10
Secondary: 20F55

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 5 • 2018
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