DOI: 10.3390/sym18101743 ISSN: 2073-8994
Langlands Duality and Invariant Differential Operators: The Case SL(2n+1)
V. K. DobrevRecently we started building a bridge between two cases of Langlands duality. The latter is one of the most influential topics in mathematical research. It has many different appearances and influential subtopics. Yet there is a topic that, until now, has seemed unrelated to the Langlands program. That is the topic of invariant differential operators. It is strange since both items are deeply rooted in Harish–Chandra’s representation theory of semisimple Lie groups. Earlier, we studied the case of the group SL(2n,R). In the present paper we deal with the group SL(2n+1,R). The two groups just mentioned are similar, but their representation theories are rather different.