Involve: A Journal of Mathematics
- Volume 11, Number 5 (2018), 721-733.
On the minuscule representation of type $B_n$
We study the action of the Weyl group of type acting as permutations on the set of weights of the minuscule representation of type (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.
Involve, Volume 11, Number 5 (2018), 721-733.
Received: 23 April 2014
Revised: 6 November 2017
Accepted: 20 November 2017
First available in Project Euclid: 12 April 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 17B10: Representations, algebraic theory (weights)
Secondary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]
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
- GAP code.