1 results
Unitary representations of type B rational Cherednik algebras and crystal combinatorics
- Part of
-
- Journal:
- Canadian Journal of Mathematics / Volume 75 / Issue 1 / February 2023
- Published online by Cambridge University Press:
- 29 September 2021, pp. 140-169
- Print publication:
- February 2023
-
- Article
-
- You have access
- HTML
- Export citation
-
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.
