Fuzzy complex Grassmannians and quantization of line bundles |
| |
Authors: | Majdi Ben Halima Tilmann Wurzbacher |
| |
Institution: | 1.Faculté des Sciences de Sfax,Département de Mathématiques,Sfax,Tunisia;2.Laboratoire de Mathématiques et Applications de Metz,Université Paul Verlaine-Metz et C.N.R.S.,Metz,France |
| |
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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|