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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.
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: May 29, 2009
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