Normalizers of irreducible subfactors
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We consider normalizers of an infinite index irreducible inclusion N M of II 1 factors. Unlike the finite index setting, an inclusion u N u * N can be strict, forcing us to also investigate the semigroup of one-sided normalizers. We relate these one-sided normalizers of N in M to projections in the basic construction and show that every trace one projection in the relative commutant N M, e N is of the form u * e N u for some unitary u M with u N u * N generalizing the finite index situation considered by Pimsner and Popa. We use this to show that each normalizer of a tensor product of irreducible subfactors is a tensor product of normalizers modulo a unitary. We also examine normalizers of infinite index irreducible subfactors arising from subgroup-group inclusions H G. Here the one-sided normalizers arise from appropriate group elements modulo a unitary from L (H). We are also able to identify the finite trace L (H)-bimodules in 2 (G) as double cosets which are also finite unions of left cosets. 2008 Elsevier Inc. All rights reserved.