A Characterization of right coideals of quotient type and its application to classification of Poisson boundaries

Let $G$ be a co-amenable compact quantum group. We show that a right coideal of $G$ is of quotient type if and only if it is the range of a conditional expectation preserving the Haar state and is globally invariant under the left action of the dual discrete quantum group. We apply this result to theory of Poisson boundaries introduced by Izumi for discrete quantum groups and generalize a work of Izumi-Neshveyev-Tuset on $SU_q(N)$ for co-amenable compact quantum groups with the commutative fusion rules. More precisely, we prove that the Poisson integral is an isomorphism between the Poisson boundary and the right coideal of quotient type by maximal quantum subgroup of Kac type. In particular, the Poisson boundary and the quantum flag manifold are isomorphic for any q-deformed classical compact Lie group.Comment: 28 pages, Remark 4.9 adde

Normalisers of irreducible subfactors

We consider normalizers of an infinite index irreducible inclusion Nsubset of or equal toM of II1 factors. Unlike the finite index setting, an inclusion uNu*subset of or equal toN 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′∩left angle bracketM,eNright-pointing angle bracket is of the form u*eNu for some unitary uset membership, variantM with uNu*subset of or equal toN 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 Hsubset of or equal toG. 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 ℓ2(G) as double cosets which are also finite unions of left cosets

Solitons in Affine and Permutation Orbifolds

We consider properties of solitons in general orbifolds in the algebraic quantum field theory framework and constructions of solitons in affine and permutation orbifolds. Under general conditions we show that our construction gives all the twisted representations of the fixed point subnet. This allows us to prove a number of conjectures: in the affine orbifold case we clarify the issue of ``fixed point resolutions''; in the permutation orbifold case we determine all irreducible representations of the orbifold, and we also determine the fusion rules in a nontrivial case, which imply an integral property of chiral data for any completely rational conformal net.Comment: Latex, 48 pages, minor style correction

The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants

We determine the Nakayama automorphism of the almost Calabi-Yau algebra A associated to the braided subfactors or nimrep graphs associated to each SU(3) modular invariant. We use this to determine a resolution of A as an A-A bimodule, which will yield a projective resolution of A.Comment: 46 pages which constitutes the published version, plus an Appendix detailing some long calculations. arXiv admin note: text overlap with arXiv:1110.454

Compact Hypergroups from Discrete Subfactors

Conformal inclusions of chiral conformal field theories, or more generally inclusions of quantum field theories, are described in the von Neumann algebraic setting by nets of subfactors, possibly with infinite Jones index if one takes non-rational theories into account. With this situation in mind, we study in a purely subfactor theoretical context a certain class of braided discrete subfactors with an additional commutativity constraint, that we call locality, and which corresponds to the commutation relations between field operators at space-like distance in quantum field theory. Examples of subfactors of this type come from taking a minimal action of a compact group on a factor and considering the fixed point subalgebra. We show that to every irreducible local discrete subfactor $\mathcal{N}\subset\mathcal{M}$ of type ${I\!I\!I}$ there is an associated canonical compact hypergroup (an invariant for the subfactor) which acts on $\mathcal{M}$ by unital completely positive (ucp) maps and which gives $\mathcal{N}$ as fixed points. To show this, we establish a duality pairing between the set of all $\mathcal{N}$-bimodular ucp maps on $\mathcal{M}$ and a certain commutative unital $C^*$-algebra, whose spectrum we identify with the compact hypergroup. If the subfactor has depth 2, the compact hypergroup turns out to be a compact group. This rules out the occurrence of compact \emph{quantum} groups acting as global gauge symmetries in local conformal field theory.Comment: 58 page

Pseudoacromegaly

© 2018 Elsevier Inc. Individuals with acromegaloid physical appearance or tall stature may be referred to endocrinologists to exclude growth hormone (GH) excess. While some of these subjects could be healthy individuals with normal variants of growth or physical traits, others will have acromegaly or pituitary gigantism, which are, in general, straightforward diagnoses upon assessment of the GH/IGF-1 axis. However, some patients with physical features resembling acromegaly – usually affecting the face and extremities –, or gigantism – accelerated growth/tall stature – will have no abnormalities in the GH axis. This scenario is termed pseudoacromegaly, and its correct diagnosis can be challenging due to the rarity and variability of these conditions, as well as due to significant overlap in their characteristics. In this review we aim to provide a comprehensive overview of pseudoacromegaly conditions, highlighting their similarities and differences with acromegaly and pituitary gigantism, to aid physicians with the diagnosis of patients with pseudoacromegaly.PM is supported by a clinical fellowship by Barts and the London Charity. Our studies on pituitary adenomas and related conditions received support from the Medical Research Council, Rosetrees Trust and the Wellcome Trust

Representing Multipliers of the Fourier Algebra on Non-Commutative L-p Spaces

We show that the multiplier algebra of the Fourier algebra on a locally compact group G can be isometrically represented on a direct sum on non-commutative Lp spaces associated to the right von Neumann algebra of G. If these spaces are given their canonical Operator space structure, then we get a completely isometric representation of the completely bounded multiplier algebra. We make a careful study of the non-commutative Lp spaces we construct, and show that they are completely isometric to those considered recently by Forrest, Lee and Samei; we improve a result of theirs about module homomorphisms. We suggest a definition of a Figa-Talamanca–Herz algebra built out of these non-commutative Lp spaces, say Ap(ˆG). It is shown that A2(ˆG) is isometric to L1(G), generalising the abelian situation