Article contents
Unitary representations of type B rational Cherednik algebras and crystal combinatorics
Published online by Cambridge University Press: 29 September 2021
Abstract
We compare crystal combinatorics of the level $2$ Fock space with the classification of unitary irreducible representations of type B rational Cherednik algebras to study how unitarity behaves under parabolic restriction. We show that the crystal operators that remove boxes preserve the combinatorial conditions for unitarity, and that the parabolic restriction functors categorifying the crystals send irreducible unitary representations to unitary representations. Furthermore, we find the supports of the unitary representations.
Keywords
- Type
- Article
- Information
- Copyright
- © Canadian Mathematical Society 2021
Footnotes
Part of this work was carried out under the auspices of the grant SFB-TRR 195.
References
- 1
- Cited by