Related papers: Fusion Rings of Loop Group Representations

We determine all genuine special unipotent representations of real spin groups and quaternionic spin groups, and show in particular that all of them are unitarizable. We also show that there are no genuine special unipotent representations…

We enumerate the number of complex irreducible representations of each degree of general unitary groups of degree 4 over principal ideal rings of length 2.

We obtain results describing the behavior of the action of rotation generators on polynomials over a commutative ring. We also explore harmonic polynomials in a purely algebraic setting.

It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras and can be seen as a preliminary step to…

By the theory of elliptic curves, we study the integers representable as the product of the sum of four integers with the sum of their reciprocals and give a sufficient condition for the integers with a positive representation.

We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…

This is a survey of results on partially commutative groups and partially commutative algebras.

We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…

We prove a Mackey formula for representations of finite groups of Lie type, in the case where the groups come from disconnected reductive groups.

We show that the quotients of Wang and Van Daele's universal quantum groups by their centers are simple in the sense that they have no normal quantum subgroups, thus providing the first examples of simple compact quantum groups with…

We study the interpolation group whose elements are suitable pairs of formal power series. This group has a faithful representation into infinite lower triangular matrices and carries thus a natural structure as a Lie group. The matrix…

We present an overview of the close analogies between the character rings of finite groups and the fusion rings of rational conformal models, which follow from general principles related to orbifold deconstruction.

In a previous paper the author constructed biinvariant measures (possibly having values in a line bundle) for a loop group LK (with compact simply connected K) acting on the formal completion of its complexification LG. One motivation for…

A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoids can be regarded as manifolds endowed with a type of…

We give the classification of the positive energy (lowest weight) unitary irreducible representations of the superalgebras osp(1|2n,R).

Calculations in Loop Quantum Gravity (LQG) and spin-foams theory rely heavily on group theory of SU(2) and SL(2,C). Even though many monographs exist devoted to this theory, the different tools needed (e.g. representation theory, harmonic…

We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on…

This article surveys the application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems. The common thread in the discussion is the construction of quantum fields using…

We give a general construction for right conjugacy closed loops, using $GL(2,q)$ for $q$ a prime power. Under certain conditions, the loops constructed are simple, giving the first general construction for finite, simple right conjugacy…

We sketch a simplification of proofs of old results on the arithmeticity of the group generated by opposing integral unipotent radicals in higher rank arithmetic groups