## Involve: A Journal of Mathematics

• Involve
• Volume 11, Number 5 (2018), 721-733.

### On the minuscule representation of type $B_n$

#### 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.

#### Article information

Source
Involve, Volume 11, Number 5 (2018), 721-733.

Dates
Revised: 6 November 2017
Accepted: 20 November 2017
First available in Project Euclid: 12 April 2018

https://projecteuclid.org/euclid.involve/1523498539

Digital Object Identifier
doi:10.2140/involve.2018.11.721

Mathematical Reviews number (MathSciNet)
MR3784022

Zentralblatt MATH identifier
06866579

#### Citation

Cook, William J.; Hughes, Noah A. On the minuscule representation of type $B_n$. Involve 11 (2018), no. 5, 721--733. doi:10.2140/involve.2018.11.721. https://projecteuclid.org/euclid.involve/1523498539

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• GAP code.