Highest weight Harish-Chandra supermodules and their geometric realizations. I. The infinitesimal theory

Abstract

In this series of papers we want to discuss the highest weight ${\mathfrak{k}}_r$-finite representations of the pair $({\mathfrak{g}}_r,{\mathfrak{k}}_r)$ consisting of ${\mathfrak{g}}_r$, a real form of a complex basic Lie superalgebra of classical type $\mathfrak{g}$ ($\mathfrak{g}\ne A(n,n)$), and the maximal compact subalgebra ${\mathfrak{k}}_r$ of ${\frak} g_{r,0}$. These representations will be concretely realized through spaces of sections of holomorphic vector bundles on the associated Hermitian superspaces. In this part we shall discuss only the infinitesimal theory of the pair $({\mathfrak{g}}_r,{\mathfrak{k}}_r)$. We treat the global theory in subsequent papers of the series.

The material in this paper appears in the replacement of arXiv:1511.01420

References in corpus (2)

• Super Distributions, Analytic and Algebraic Super Harish-Chandra pairs
• Algebraic supergroups with Lie superalgebras of classical type