Euler-Poincaré pairing, Dirac index and elliptic pairing for Harish-Chandra modules

Generalized Harish-Chandra Modules

Globalizations of Harish-chandra Modules

Harish-chandra Modules for Quantum Symmetric Pairs

Let U denote the quantized enveloping algebra associated to a semisimple Lie algebra. This paper studies Harish-Chandra modules for the recently constructed quantum symmetric pairs U ,B in the maximally split case. Finite-dimensional U -modules are shown to be Harish-Chandra as well as the B-unitary socle of an arbitrary module. A classification of finite-dimensional spherical modules analogous...

Cramped Subgroups and Generalized Harish-chandra Modules

Let G be a reductive complex Lie group with Lie algebra g. We call a subgroup H ⊂ G cramped if there is an integer b(G,H) such that each finite-dimensional representation of G has a non-trivial invariant subspace of dimension less than b(G,H). We show that a subgroup is cramped if and only if the moment map T ∗(K/L) → k∗ is surjective, where K and L are compact forms of G and H. We will use thi...

Smooth Fréchet Globalizations of Harish-chandra Modules

We give an alternative proof of the Casselman–Wallach globalization theorem. The approach is based on lower bounds for matrix coefficients on a reductive group.