Alexandra Utiralova, Serina Hu
Published 2021-07-07Version 1
We continue the study of Harish-Chandra bimodules in the setting of the Deligne categories $\mathrm{Rep}(G_t)$, that was started in the previous work of the first author (arXiv:2002.01555). 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 $\mathrm{Rep}(G_t)$. 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 a question posed by Pavel Etingof in one of his works.
Deligne categories and reduced Kronecker coefficients
Deligne categories as limits in rank and characteristic
Functors between Deligne categories and rings of numbers $\sum_{n\in \mathbb Z_+} a_n\binom{s}{n}$ where $s\in \overline{\mathbb Q}$ and $a_n \in \mathbb Z_+$
![QR code for arXiv:2107.03173 [math.RT]](http://oss.arxitics.com/images/favicon.svg)