Related papers: su(3)k fusion coefficients
This is the second of two articles devoted to an exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper focuses on fusion rules, using the machinery developed for tensor products in…
We present a closed-form solution for n-th term of a general three-term recurrence relation with arbitrary given n-dependent coefficients. The derivation and corresponding proof are based on two approaches, which we develop and describe in…
We study tensor products of infinite dimensional representations (not corepresentations) of the $\mathrm{SU}(2)$ quantum group. Eigenvectors of certain self-adjoint elements are obtained, and coupling coefficients between different…
We find the solution of the $\hat{sl}(3)_k$ singular vector decoupling equations on 3-point functions for the particular case when one of the fields is of weight $w_0\cdot k\Lambda_0$. The result is a function with non-trivial singularities…
We provide a formula for the SU(3) Casson invariant for 3-manifolds given as the connected sum of two integral homology 3-spheres.
We give a geometric description of the fusion rules of the affine Lie algebra su(2)_k at a positive integer level k in terms of the k-th power of the basic gerbe over the Lie group SU(2). The gerbe can be trivialised over conjugacy classes…
We calculate the form factors for the heavy-to-light transitions $B\rightarrow \pi,K $ by means of QCD sum rules using $\pi$ and $K$ light-cone wave functions. Higher twist contributions as well as gluonic corrections are taken into…
It was recently proven that the total multiplicity in the decomposition into irreducibles of the tensor product lambda x mu of two irreducible representations of a simple Lie algebra is invariant under conjugation of one of them; at a given…
Fusion of positive energy representations is defined using Connes' tensor product for bimodules over a von Neumann algebra. Fusion is computed using the analytic theory of primary fields and explicit solutions of the Knizhnik-Zamolodchikov…
A presentation of the problem of calculating the vector coupling coefficients for $SU3 \supset SU2 \otimes U1$ is made, in the spirit of traditional treatments of SU2 coupling. The coefficients are defined as the overlap matrix element…
Binomial coefficients and central trinomial coefficients play important roles in combinatorics. Let $p>3$ be a prime. We show that $$T_{p-1}\equiv\left(\frac p3\right)3^{p-1}\ \pmod{p^2},$$ where the central trinomial coefficient $T_n$ is…
We consider three-point couplings in simple Lie algebras -- singlets in triple tensor products of their integrable highest weight representations. A coupling can be expressed as a linear combination of products of finitely many elementary…
We study how to use smooth, compact toric varieties for supersymmetric $AdS_4$ flux compactifications using tools of SU(3) structures, similar to $CP3$ solution. A non-vanishing globally well defined complex 3-form plays a key role in such…
Group elements of SU(2) are expressed in closed form as finite polynomials of the Lie algebra generators, for all definite spin representations of the rotation group. The simple explicit result exhibits connections between group theory,…
The confluent SUSY QM usually involves a second-order SUSY transformation where the two factorization energies converge to a single value. In order to achieve it, one generally needs to solve an indefinite integral, which limits the actual…
Affine su(3) and su(4) fusion multiplicities are characterised as discretised volumes of certain convex polytopes. The volumes are measured explicitly, resulting in multiple sum formulas. These are the first polytope-volume formulas for…
We develop simple computational techniques for constructing all possible SU(3) representations in terms of irreducible SU(3) Schwinger bosons. We show that these irreducible Schwinger oscillators make SU(3) representation theory as simple…
We introduced a non-symmetric tensor product of any two states or any two representations of Cuntz-Krieger algebras associated with a certain non-cocommutative comultiplication in previous our work. In this paper, we show that a certain set…
We use two non-perturbative methods to obtain the anisotropy derivatives of the coupling constants (the anisotropy coefficients) of SU(3) lattice gauge theory. These coefficients appear in the derivative formulae for the energy density and…
In this paper we define a quantum version of the ``fusion'' tensor product of two representations of an affine Kac-Moody algebra.It is replaced by what we call fusion action of the category of finite-dimensional representations of quantum…