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Unitary representations of type B rational Cherednik algebras and crystal combinatorics
- Source :
- Canadian Journal of Mathematics. 75:140-169
- Publication Year :
- 2021
- Publisher :
- Canadian Mathematical Society, 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. First, we show that any finite-dimensional unitary irreducible representation of such an algebra is labeled by a bipartition consisting of a rectangular partition in one component and the empty partition in the other component. This is a new proof of a result that can be deduced from theorems of Montarani and Etingof-Stoica. Second, 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. Third, we find the supports of the unitary representations.<br />This paper supersedes arXiv:1907.00919 and contains that paper as a subsection. 35 pages, some color figures
- Subjects :
- Functor
Unitarity
General Mathematics
Type (model theory)
Unitary state
Fock space
Combinatorics
Irreducible representation
FOS: Mathematics
Mathematics - Combinatorics
Partition (number theory)
Component (group theory)
Combinatorics (math.CO)
Representation Theory (math.RT)
Mathematics::Representation Theory
Mathematics - Representation Theory
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 75
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....550fa75d0eb37642d3f8009e401d7e1a