Geodesic
Unitary representations of type B rational Cherednik algebras and crystal combinatorics
Canadian journal of mathematics, Tome 75 (2023) no. 1, pp. 140-169

Voir la notice de l'article provenant de la source Cambridge

DOI

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.
DOI : 10.4153/S0008414X21000559
Mots-clés : rational Cherednik algebra, unitary representation, Fock space, affine Lie algebra crystal, combinatorial representation theory 
Norton, Emily. Unitary representations of type B rational Cherednik algebras and crystal combinatorics. Canadian journal of mathematics, Tome 75 (2023) no. 1, pp. 140-169. doi: 10.4153/S0008414X21000559
@article{10_4153_S0008414X21000559,
     author = {Norton, Emily},
     title = {Unitary representations of type {B} rational {Cherednik} algebras and crystal combinatorics},
     journal = {Canadian journal of mathematics},
     pages = {140--169},
     year = {2023},
     volume = {75},
     number = {1},
     doi = {10.4153/S0008414X21000559},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000559/}
}
TY  - JOUR
AU  - Norton, Emily
TI  - Unitary representations of type B rational Cherednik algebras and crystal combinatorics
JO  - Canadian journal of mathematics
PY  - 2023
SP  - 140
EP  - 169
VL  - 75
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000559/
DO  - 10.4153/S0008414X21000559
ID  - 10_4153_S0008414X21000559
ER  - 
%0 Journal Article
%A Norton, Emily
%T Unitary representations of type B rational Cherednik algebras and crystal combinatorics
%J Canadian journal of mathematics
%D 2023
%P 140-169
%V 75
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000559/
%R 10.4153/S0008414X21000559
%F 10_4153_S0008414X21000559

Cité par Sources :