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ISSN 1088-6850(e) ISSN 0002-9947(p)

On the -compact groups corresponding to the -adic reflection groups

Author: Natàlia Castellana
Journal: Trans. Amer. Math. Soc. 358 (2006), 2799-2819
MSC (2000): Primary 55R35, 14E20; Secondary 55R40, 20D20
Posted: February 6, 2006
MathSciNet review: 2216246
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Abstract: There exists an infinite family of -compact groups whose Weyl groups correspond to the finite -adic pseudoreflection groups of family 2a in the Clark-Ewing list. In this paper we study these -compact groups. In particular, we construct an analog of the classical Whitney sum map, a family of monomorphisms and a spherical fibration which produces an analog of the classical -homomorphism. Finally, we also describe a faithful complexification homomorphism from these -compact groups to the -completion of unitary compact Lie groups.

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