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Zonal Functions for the Unitary Groups and Applications to Hermitian Lattices

✍ Scribed by Christine Bachoc; Gabriele Nebe

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 218 KB
Volume: 96
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2002.2785

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✦ Synopsis

We study the decomposition of the space L 2 ðS nÀ1 Þ under the actions of the complex and quaternionic unitary groups. We give an explicit basis for the space of zonal functions, which in the second case takes account of the action of the group of quaternions of norm 1. We derive applications to hermitian lattices. # 2002 Elsevier Science (USA)

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