${\mathfrak{sl}}_2$-Harish-Chandra modules for ${\mathfrak{sl}}_2⋉L(4)$

Abstract

We use analogues of Enright's and Arkhipov's functors to determine the quiver and relations for a category of ${\mathfrak{sl}}_2⋉L(4)$-modules which are locally finite (and with finite multiplicities) over ${\mathfrak{sl}}_2$. We also outline serious obstacles to extend our result to ${\mathfrak{sl}}_2⋉L(k)$, for $k>4$.

References in corpus (1)

• Category O for Takiff sl_2