Separating Vector Bundle Sections by Invariant Means

2012/10/19 by Gestur Olafsson, Joseph A. Wolf, Olafsson, Gestur +1
Mathematics · #32L10 (Secondary) #32L25 (Primary) 22E46 #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.DG #math.GR #math.RT #msc:22E46 #msc:32L10 #msc:32L25

paper · pdf · doi:10.48550/arxiv.1210.5494

arxiv created 2012/10/19 · arxiv updated 2012/10/22

Abstract

We sharpen the construction of representation space in the paper "Principal Series Representations of Infinite Dimensional Lie Groups II: Construction of Induced Representations". We show that the principal series representation spaces constructed there, are completions of spaces of sections of Hilbert bundles rather than completions of quotient spaces of sections.

Related

• Principal series representations of infinite dimensional Lie groups, II: Construction of induced representations
• Minuscule representations, invariant polynomials, and spectral covers
• Vector bundles, linear representations, and spectral problems
• Principal Series Representations of Infinite Dimensional Lie Groups, I: Minimal Parabolic Subgroups
• Dimension of the space of intertwining operators from degenerate principal series representations