Related papers: Fusion Rings of Loop Group Representations
We present an algorithm for an efficient calculation of the fusion rules of twisted representations of untwisted affine Lie algebras. These fusion rules appear in WZW orbifold theories and as annulus coefficients in boundary WZW theories;…
The projective unitary group PU(n) is the quotient of the unitary group U(n) by its center. We compute the integral cohomology ring of PU(n) using explicit constructed generators.
We present an extremely elementary construction of the simple Lie algebras over the complex numbers in all of their minuscule representations, using the vertices of various polytopes. The construction itself requires no complicated…
Since the gauge group underlying 2+1-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately…
We study the relation between representations of certain infinite-dimensional Lie groups and those of the associated conformal nets. For a chiral conformal net extending the net generated by the vacuum representation of a loop group or…
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…
A representation of an object in a category is an abelian group in the corresponding comma category. In this paper we derive the formulas describing linear representations of objects in the category of formal loops and apply them to obtain…
We discuss a simple procedure for computing one-loop quantum energies of any static field configuration that depends non-trivially on only a single spatial coordinate. We specifically focus on domain wall-type field configurations that…
We examine the representation of numbers as the sum of two squares in $\mathbb{Z}_n$ for a general positive integer $n$. Using this information we make some comments about the density of positive integers which can be represented as the sum…
For a commutative finite $\mathbb{Z}$-algebra, i.e., for a commutative ring $R$ whose additive group is finitely generated, it is known that the group of units of $R$ is finitely generated, as well. Our main results are algorithms to…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
A formula to calculate the quantum fluctuations of energy in small subsystems of a hot and relativistic gas is derived. We find an increase in fluctuations for subsystems of small sizes, but we agrees with the energy fluctuations in the…
The fusion rules and modular matrix of a rational conformal field theory obey a list of properties. We use these properties to classify rational conformal field theories with not more than six primary fields and small values of the fusion…
Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been…
In this paper, first we introduce the notion of quadratic Rota-Baxter Lie algebras of arbitrary weight, and show that there is a one-to-one correspondence between factorizable Lie bialgebras and quadratic Rota-Baxter Lie algebras of nonzero…
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.
For any root system corresponding to a semisimple simply-laced Lie algebra a logarithmic CFT is constructed. Characters of irreducible representations were calculated in terms of theta functions.
Toda equations associated with twisted loop groups are considered. Such equations are specified by Z-gradations of the corresponding twisted loop Lie algebras. The classification of Toda equations related to twisted loop Lie algebras with…
We study fusion rings for degenerate minimal models ($p=q$ case) for N=0 and N=1 (super)conformal algebras. We consider a distinguished family of modules at the level $c=1$ and $c=3/2$ and show that the corresponding fusion rings are…
Starting from square-integrable wave functions on a Lie group, we build an invertible Fourier transform mapping them on wave functions on the dual of the Lie algebra. This is a group-theoretic version of the map from position space to…