Related papers: Reflection positivity for the circle group

We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…

We obtain some new results on classical solutions of two dimensional Euclidean sigma models. From earlier work of Din-Zakrzewski, Glaser-Stora, and numerous differential geometers, one knows explicit solutions in the case of the…

We construct projective unitary representations of the smooth Deligne cohomology group of a compact oriented Riemannian manifold of dimension 4k+1, generalizing positive energy representations of the loop group of the circle. We also…

Steinberg showed that when a finite reflection group acts on a real or complex vector space of finite dimension, the Jacobian determinant of a set of basic invariants factors into linear forms which define the reflecting hyperplanes. This…

We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the…

We describe surprising relationships between automorphic forms of various kinds, imaginary quadratic number fields and a certain system of six finite groups that are parameterised naturally by the divisors of twelve. The Mathieu group…

We use a functional approach to study various aspects of the quantum effective dynamics of moving, planar, dispersive mirrors, coupled to scalar or Dirac fields, in different numbers of dimensions. We first compute the Euclidean effective…

We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of…

Let $\Gamma$ be a discrete group. To every ideal in $\ell^{\infty}(\G)$ we associate a C$^*$-algebra completion of the group ring that encapsulates the unitary representations with matrix coefficients belonging to the ideal. The general…

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in…

We give a necessary and sufficient condition, in terms of a certain reflection principle, for every unconditionally closed subset of a group G to be algebraic. As a corollary, we prove that this is always the case when G is a direct product…

We introduce a notion of {\em cyclic Schur-positivity} for sets of permutations, which naturally extends the classical notion of Schur-positivity, and it involves the existence of a bijection from permutations to standard Young tableaux…

We prove that united K-theory is a surjective functor from the category of real simple purely infinite C*-algebras to the cateogry of countable acyclic CRT-modules.

We propose a new axiom system for unitary quantum field theories on curved space-time backgrounds, by postulating that the partition function and the correlators extend analytically to a certain domain of complex-valued metrics. Ordinary…

We define and study entanglement of continuous positive definite functions on products of compact groups. We formulate and prove an infinite-dimensional analog of Horodecki Theorem, giving a necessary and sufficient criterion for…

We describe the space-time model of a uniformly rotating frame of reference satisfying the Helmholtz free mobility postulate, as we implemented it in a preceding article \cite{Bel1}, and we discuss the implications of this model as it…

We provide an equivariant description/classification of all complete (compact or not) non-negatively curved manifolds M together with a co-compact action by a reflection group W, and moreover, classify such W. In particular, we show that…

Chevalley's theorem and it's converse, the Sheppard-Todd theorem, assert that finite reflection groups are distinguished by the fact that the ring of invariant polynomials is freely generated. We show that in the Euclidean case, a weaker…

Convolution admits a natural formulation as a functional operation on matrices. Motivated by the functional and entrywise calculi, this leads to a framework in which convolution defines a matrix transform that preserves positivity. Within…

We revisit and extend results by Ueltschi [19] on the application of reflection positivity to loop models with $\theta \in \mathbb{N}_{\geq 2}$. By exploiting additional flexibility in the method, we prove the existence of long loops over a…