We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Harish–Chandra Bimodules of Finite K-type in Deligne Categories.
- Authors
Utiralova, Alexandra
- Abstract
We continue the study of Harish–Chandra bimodules in the setting of the Deligne categories |$\operatorname {Rep}(G_{t})$| that we started in [ 17 ]. In this work, we construct a family of Harish–Chandra bimodules that generalize simple finite dimensional bimodules in the classical case. It turns out that they have finite |$K$| -type, which is a non-vacuous condition for the Harish–Chandra bimodules in |$\operatorname {Rep}(G_{t})$|. The full classification of (simple) finite |$K$| -type bimodules is yet unknown. This construction also yields some examples of central characters |$\chi $| of the universal enveloping algebra |$U(\mathfrak {g}_{t})$| for which the quotient |$U_{\chi }$| is not simple, and, thereby, it allows us to partially solve Problem 3.23 posed in [ 10 ].
- Subjects
UNIVERSAL algebra; PROBLEM solving
- Publication
IMRN: International Mathematics Research Notices, 2023, Vol 2023, Issue 18, p15766
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnac327