×

The invariant holonomic system on a semisimple Lie group. (English) Zbl 0704.22008

Algebraic analysis, Pap. Dedicated to Prof. Mikio Sato on the Occas. of his Sixtieth Birthday, Vol. 1, 277-286 (1989).
[For the entire collection see Zbl 0665.00008.]
Let G be a connected reductive algebraic group defined over \({\mathbb{C}}\), and let \({\mathfrak G}\) be its Lie algebra. The center \({\mathfrak Z}({\mathfrak G})\) of the universal enveloping algebra is identified with the ring of bi- invariant differential operators on G. Denote by \({\mathcal D}_ G\) the ring of differential operators on G. If \(\chi\) : \({\mathfrak Z}({\mathfrak G})\to {\mathbb{C}}\) is a character, let \({\mathcal M}_{\chi}\) be the \({\mathcal D}_ G\)- module \({\mathcal D}_ G/({\mathcal D}_ GAd({\mathfrak G})+\sum_{P\in {\mathfrak Z}({\mathfrak G})}{\mathcal D}_ G(P-\chi (P)))\). The author proves various results on \({\mathcal M}_{\chi}\) and on the \({\mathcal D}_ G\)-module \({\mathcal D}_ G/{\mathcal D}_ GAd({\mathfrak G})\).
Reviewer: P.Godin

MSC:

22E30 Analysis on real and complex Lie groups
22E60 Lie algebras of Lie groups
32C38 Sheaves of differential operators and their modules, \(D\)-modules
22E46 Semisimple Lie groups and their representations
32A45 Hyperfunctions
58J15 Relations of PDEs on manifolds with hyperfunctions

Citations:

Zbl 0665.00008