# A proof of Casselman's comparison theorem for standard minimal parabolic subalgebra

@inproceedings{Li2021APO, title={A proof of Casselman's comparison theorem for standard minimal parabolic subalgebra}, author={Ning Li and Gang Liu and Jun Yu}, year={2021} }

Let G be a real linear reductive group and K be a maximal compact subgroup. Let P be a minimal parabolic subgroup of G with complexified Lie algebra p, and n be its nilradical. In this paper we show that: for any admissible finitely generated moderate growth smooth Fréchet representation V of G, the inclusion VK ⊂ V induces isomorphisms Hi(n, VK) ∼= Hi(n, V ) (i ≥ 0), where VK denotes the (g,K) module of K finite vectors in V . This is called Casselman’s comparison theorem ([12]). As a…

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