Affiliation:
1. Massachusetts Institute of Technology , Department of Mathematics, 77 Massachusetts Ave, Building 2, Cambridge, MA 02139
Abstract
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].
Publisher
Oxford University Press (OUP)
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