Related papers: Fusion Rings of Loop Group Representations

Quantum theory can be formulated as a theory of operations, more specific, of complex represented operations from real Lie groups. Hilbert space eigenvectors of acting Lie operations are used as states or particles. The simplest simple Lie…

We survey some of our old results given in [CE95] and [CE10] and present some new ones in the last three sections.We survey some of our old results given in [CE95] and [CE10] and present some new ones in the last three sections.

We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible…

We determine for which known finite simple groups $G$ and which primes $p$ the $p$-fusion system of $G$ is simple. This means first collecting together the results that were already known (and correcting two errors made in an earlier study…

We find the fusion rules for the quantum analogues of the complex reflection groups $H_n^s=\mathbb Z_s\wr S_n$. The irreducible representations can be indexed by the elements of the free monoid $\mathbb N^{*s}$, and their tensor products…

In this article we summarize and describe the recently found transforms for theories of connections modulo gauge transformations associated with compact gauge groups. Specifically, we put into a coherent picture the so-called loop…

We determine the ring structure of the loop homology of some global quotient orbifolds. We can compute by our theorem the loop homology ring with suitable coefficients of the global quotient orbifolds of the form $[M/G]$ for $M$ being some…

The main notions of the quantum groups: coproduct, action and coaction, representation and corepresentation are discussed using simplest examples: $GL_q(2)$, $sl_q(2)$, $q$-oscillator algebra ${\cal A}(q)$, and reflection equation algebra.…

We construct a commutative version of the group ring and show that it allows one to translate questions about the normal generation of groups into questions about the generation of ideals in commutative rings. We demonstrate this with an…

Fusion is defined for arbitrary lowest weight representations of $W$-algebras, without assuming rationality. Explicit algorithms are given. A category of quasirational representations is defined and shown to be stable under fusion.…

An idea to present a classical Lie group of positive dimension by generators and relations sounds dubious, but happens to be fruitful. The isometry groups of classical geometries admit elegant and useful presentations by generators and…

We develop methods of computation of the Brauer-Picard groups of fusion categories and apply them to compute such groups for several classes of fusion categories of prime power dimension: representation categories of elementary abelian…

We describe all fusion subcategories of the representation category of a twisted quantum double of a finite group. In view of the fact that every group-theoretical braided fusion category can be embedded into a representation category of a…

Generalized Lie-Cartan theorem for linear birepresentations of an analytic Moufang loop is considered. The commutation relations of the generators of the birepresentation were found. In particular, the Lie algebra of the multiplication…

We classify all three-dimensional connected topological loops such that the group topologically generated by their left translations is the four-dimensional connected Lie group $G$ which has trivial center and precisely two one-dimensional…

Let g be a semisimple Lie algebra over the complex numbers. Fix a positive integer l (called the level). Let R(l,g) be the fusion algebra at level l. Then, there is an algebra homomorphism from the representation ring R(g) of g to R(l,g).…

Using a pointwise version of Fej\'{e}r's theorem about Fourier series, we obtain two formulae related to the series representations of positive integral powers of $\pi$. We also check the correctness of our formulae by the applications of…

We give a classification of unitary representations of certain Polish, not necessarily locally compact, groups: the groups of all measurable functions with values in the circle and the groups of all continuous functions on compact, second…

Orbits of coadjoint representations of classical compact Lie groups have a lot of applications. They appear in representation theory, geometrical quantization, theory of magnetism, quantum optics etc. As geometric objects the orbits were…

We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…