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

2015/03/12 by Carmeli, C., Fioresi, R., Varadarajan, V. S.
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1503.03828

Abstract

In this series of papers we want to discuss the highest weight \frak k_r-finite representations of the pair (\frak g_r,\frak k_r) consisting of \frak g_r, a real form of a complex basic Lie superalgebra of classical type \frak g (\frak g≠ A(n,n)), and the maximal compact subalgebra \frak 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 (\frak g_r, \frak k_r). We treat the global theory in subsequent papers of the series.

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