2017/08/14 by Tsao-Hsien Chen, Chen, Tsao-Hsien, Dennis Gaitsgory +3
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1708.04046
Very minor modifications, compared to previous version (to appear in Proceedings of Symposia in Pure Mathematics volume, titled "Representations of Reductive Groups")
arxiv created 2019/01/03 · arxiv updated 2019/01/04
We study the Casselman-Jacquet functor J, viewed as a functor from the (derived) category of (\mathfrakg,K)-modules to the (derived) category of (\mathfrakg,N-)-modules, N- is the negative maximal unipotent. We give a functorial definition of J as a certain right adjoint functor, and identify it as a composition of two averaging functors AvN-_!∘ AvN_*. We show that it is also isomorphic to the composition AvN-_*∘ AvN_!. Our key tool is the pseudo-identity functor that acts on the (derived) category of (twisted) D-modules on an algebraic stack.