264 research outputs found
A locally compact quantum group analogue of the normalizer of SU(1,1) in SL(2,C)
S.L. Woronowicz proved in 1991 that quantum SU(1,1) does not exist as a
locally compact quantum group. Results by L.I. Korogodsky in 1994 and more
recently by Woronowicz gave strong indications that the normalizer N of SU(1,1)
in SL(2,C) is a much better quantization candidate than SU(1,1) itself. In this
paper we show that this is indeed the case by constructing N_q, a new example
of a unimodular locally compact quantum group (depending on a parameter q) that
is a deformation of N. After defining the underlying von Neumann algebra of N_q
we use a certain class of q-hypergeometric functions and their orthogonality
relations to construct the comultiplication. The coassociativity of this
comultiplication is the hardest result to establish. We define the Haar weight
and obtain simple formulas for the antipode and its polar decomposition. As a
final result we produce the underlying C*-algebra of N_q. The proofs of all
these results depend on various properties of q-hypergeometric 1\phi1
functions.Comment: 48 pages, 1 figur
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