Highest weight Harish-Chandra supermodules and their geometric realizations

2015/11/04 by Claudio Carmeli, Carmeli, C., R. Fioresi +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1511.01420

openalex publication_date 2015/11/04 · openalex created_date 2018/09/27 · openalex updated_date 2026/07/28

Abstract

In this paper we 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, together with their geometric global realizations. These representations occur, as in the ordinary setting, in the superspaces of sections of holomorphic super vector bundles on the associated Hermitian superspaces G_r/K_r.

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