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Fuzzy complex Grassmannians and quantization of line bundles

Fuzzy complex Grassmannians and quantization of line bundles We construct by purely representation-theoretic methods fuzzy versions of an arbitrary complex Grassmannian M=Gr n (ℂ n+m ), i.e., a sequence of matrix algebras tending SU(n+m)-equivariantly to the algebra of smooth functions on M. We also show that this approximation can be interpreted in terms of the Berezin-Toeplitz quantization of M. Furthermore, we use branching rules to prove that the quantization of every complex line bundle over M is given by a SU(n+m)-equivariant truncation of the space of its L 2-sections. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

Fuzzy complex Grassmannians and quantization of line bundles

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References (28)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Mathematisches Seminar der Universität Hamburg and Springer
Subject
Mathematics; Geometry ; Topology; Number Theory; Combinatorics; Differential Geometry; Algebra
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/s12188-009-0025-0
Publisher site
See Article on Publisher Site

Abstract

We construct by purely representation-theoretic methods fuzzy versions of an arbitrary complex Grassmannian M=Gr n (ℂ n+m ), i.e., a sequence of matrix algebras tending SU(n+m)-equivariantly to the algebra of smooth functions on M. We also show that this approximation can be interpreted in terms of the Berezin-Toeplitz quantization of M. Furthermore, we use branching rules to prove that the quantization of every complex line bundle over M is given by a SU(n+m)-equivariant truncation of the space of its L 2-sections.

Journal

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals

Published: May 29, 2009

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