Related papers: The trace on projective representations of quantum…
We prove a rigidity theorem for morphisms from products of open subschemes of the projective line into solvable groups not containing a copy of $\Ga$ (for example, wound unipotent groups). As a consequence, we deduce several structural…
We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…
We develop the idea that the particles of the standard model may arise from excitations of quantum geometry. A previously proposed topological model of preons is developed so that it incorporates an unbounded number of generations. A…
The main result of this paper is the construction of a trace and a trace pairing for endomorphisms satisfying suitable conditions in a monoidal category. This construction is a common generalization of the trace for endomorphisms of…
We construct lattice gauge field theory based on a quantum group on a lattice of dimension 1. Innovations include a coalgebra structure on the connections, and an investigation of connections that are not distinguishable by observables. We…
We introduce the notion of locally trivial quantum principal bundles. The base space and total space are compact quantum spaces (unital $C^{\star}$-algebras), the structure group is a compact matrix quantum group. We prove that a quantum…
We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with…
The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group…
We categorify one half of the small quantum sl(2) at a prime root of unity. An extension of this construction to an arbitrary simply-laced case is proposed.
In this paper we study modular tensor categories (braided rigid balanced tensor categories with additional finiteness and non-degeneracy conditions), in particular, representations of quantum groups at roots of unity. We show that the…
We consider two families of categories. The first is the family of semisimple quotients of H. Andersen's tilting module categories for quantum groups of Lie type $B$ specialized at odd roots of unity. The second consists of categories…
Toric $t$-designs, or equivalently $t$-designs on the diagonal subgroup of the unitary group, are sets of points on the torus over which sums reproduce integrals of degree $t$ monomials over the full torus. Motivated by the projective…
The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group…
Tensors and traceouts are generalised, so that systems can be partitioned according to almost arbitrary logical predicates. One might have feared that the familiar interrelations between the notions of unitarity, complete positivity,…
We study some aspects of the theory of non-commutative differential calculi over complex algebras, especially over the Hopf algebras associated to compact quantum groups in the sense of S.L. Woronowicz. Our principal emphasis is on the…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
We prove that some well known compact quantum spaces like quantum tori and some quantum two-spheres do not admit a compact quantum group structure. This is achieved by considering existence of traces, characters and nuclearity of the…
The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace rule for calculating probabilities). In this paper it is shown that quantum theory can be…
There is a long history of representing a quantum state using a quasi-probability distribution: a distribution allowing negative values. In this paper we extend such representations to deal with quantum channels. The result is a convex,…
We classify the simple infinite dimensional integrable modules with finite dimensional weight spaces over the quantized enveloping algebra of an untwisted affine algebra. We prove that these are either highest (lowest) weight integrable…