On the category of Harish-Chandra block modules (Q6597524)

The author generalizes the following result of \textit{Yu. A. Drozd} et al. [NATO ASI Ser., Ser. C, Math. Phys. Sci. 424, 79--93 (1994; Zbl 0812.17007)] (dropping the assumption that \(G\) is quasicommutative): when \(G\) is a Harish-Chandra subalgebra of \(A\) the structure of Harish-Chandra \(A\)-modules can be described using information about the relationship between \(A\) and the cofinite maximal ideals of \(G\). The author introduces Harish-Chandra block modules and extend the previous result to these modules (Section 3.4).\N\NThe notion of strong Harish-Chandra block modules allows to clarify ambiguities in the work of Drozd, Futorny, and Ovsienko [loc. cit.], raised by the possibility of infinite- dimensional generalized weight spaces (Theorem 1.2).