Related papers: Fusion rules and the Patera-Sharp generating-funct…
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…
This is the first of two articles devoted to a exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit…
This is the first of two articles devoted to a comprehensive exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product…
This is an expository introduction to fusion rules for affine Kac-Moody algebras, with major focus on the algorithmic aspects of their computation and the relationship with tensor product decompositions. Many explicit examples are included…
We give a new proof of a formula for the fusion rules for type $A_2$ due to B\'egin, Mathieu, and Walton. Our approach is to symbolically evaluate the Kac-Walton algorithm.
A closed and explicit formula for all $\su{(3)}_k$ fusion coefficients is presented which, in the limit $k \rightarrow \infty$, turns into a simple and compact expression for the $su(3)$ tensor product coefficients. The derivation is based…
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…
Using the generating function of SU(n) we find the conjugate state of SU(n) basis and we find in terms of Gel'fand basis of SU(3(n-1)) the representation of the invariants of the Kronecker products of SU(n). We find a formula for the number…
The depth rule is a level truncation of tensor product coefficients expected to be sufficient for the evaluation of fusion coefficients. We reformulate the depth rule in a precise way, and show how, in principle, it can be used to calculate…
Following a recent proposal of Richard Borcherds to regard fusion as the ring-like tensor product of modules of a {\em quantum ring}, a generalization of rings and vertex operators, we define fusion as a certain quotient of the (vector…
In this article, we deeply reveal the relationship between functions $\theta$ and $\vartheta$ in an overlap function additively generated by an additive generator pair ($\theta$,$\vartheta$). Then we characterize the conditions for an…
We present an explicit conjecture for the chiral fusion algebra of critical percolation considering Virasoro representations with no enlarged or extended symmetry algebra. The representations we take to generate fusion are countably…
We state and prove product formulae for several generating functions for sequences $(a_n)_{n\ge0}$ that are defined by the property that $Pa_n+b^2$ is a square, where $P$ and $b$ are given integers. In particular, we prove corresponding…
We show how the threshold level of affine fusion, the fusion of Wess-Zumino-Witten (WZW) conformal field theories, fits into the Schubert calculus introduced by Gepner. The Pieri rule can be modified in a simple way to include the threshold…
We review some recent results on properties of tensor product and fusion coefficients under complex conjugation of one of the factors. Some of these results have been proven, some others are conjectures awaiting a proof, one of them…
We derive fusion rules for the composition of $q$-deformed classical representations (arising in tensor products of the fundamental representation) with semi-periodic representations of $SL(N)_q$ at roots of unity. We obtain full…
Many combinatorial generating functions can be expressed as combinations of symmetric functions, or extracted as sub-series and specializations from such combinations. Gessel has outlined a large class of symmetric functions for which the…
The degeneracy of the lowest weight representations of the quantum superalgebra $osp_q(1|2)$ and their tensor products at exceptional values of %when deformation parameter $q$ takes exceptional values is studied. The main features of the…
One well studied way to construct quasicrystalline tilings is via inflate-and-subdivide (a.k.a. substitution) rules. These produce self-similar tilings--the Penrose, octagonal, and pinwheel tilings are famous examples. We present a…
The application of k_t - factorization supplemented with the CCFM small-x evolution equation to heavy quark production is discussed. The b-b_bar production cross sections at the TEVATRON can be consistently described using the…