Related papers: Fusion algebra and Verlinde's formula
We prove a generalization of the Verlinde formula to fermionic rational conformal field theories. The fusion coefficients of the fermionic theory are equal to sums of fusion coefficients of its bosonic projection. In particular, fusion…
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint…
We give universal upper bounds on the relative dimensions of isotypic components of a tensor product of the linear group GL(n) representations and universal upper bounds on the relative dimensions of irreducible components of a tensor…
In this note we present a complete analysis of finite dimensional representations of the Lie superalgebra sl(2|1). This includes, in particular, the decomposition of all tensor products into their indecomposable building blocks. Our…
In this note we illustrate by a few examples the general principle: interesting algebras and representations defined over Z_+ come from category theory, and are best understood when their categorical origination has been discovered. We show…
We classify indecomposable summands of mixed tensor powers of the natural representation for the general linear supergroup up to isomorphism. We also give a formula for the characters of these summands in terms of composite supersymmetric…
In this note we calculate the fusion coefficients for minimal series representations of the N=2 superconformal algebra by using a modified Verlinde's formula, and obtain associative and commutative fusion algebras with non-negative integral…
In this paper we study modular $G$-equivariant fusion categories and their extended Verlinde algebras. We dicuss settings in which fusion rules are diagonalizable. In particular, when $G = \mathbb{Z}_{2}$ we generalize the Verlinde formula.…
The modular properties of fractional level affine sl(2)-theories and, in particular, the application of the Verlinde formula, have a long and checkered history in conformal field theory. Recent advances in logarithmic conformal field theory…
We determine the graded decompositions of fusion products of finite-dimensional irreducible representations for simple Lie algebras of rank two. Moreover, we give generators and relations for these representations and obtain as a…
Exploiting particular features of classical groups, simple constructions are given for the irreducible constituents of the tensor square of the adjoint modules and the leading terms in higher tensor powers. This provides an independent…
The space spanned by the characters of twisted affine Lie algebras admit the action of certain congruence subgroups of $SL(2,\mathbb{Z})$. By embedding the characters in the space spanned by theta functions, we study an…
This article gives a complete account of the modular properties and Verlinde formula for conformal field theories based on the affine Kac-Moody algebra sl(2) at an arbitrary admissible level k. Starting from spectral flow and the structure…
By using of Euler's difference table, we obtain simple explicit formula for the decomposition of $k$-th tensor power of adjoint representation of $A_n$ Lie algebra at $2 k \le{n+1}$.
We obtain the decomposition of the tensor space $\mathfrak{sl}_n^{\otimes k}$ as a module for $\mathfrak{sl}_n$, find an explicit formula for the multiplicities of its irreducible summands, and (when $n \ge 2k$) describe the centralizer…
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…
A thorough analysis is made of the Fourier coefficients for vector-valued modular forms associated to three-dimensional irreducible representations of the modular group. In particular, the following statement is verified for all but a…
In this paper we prove that every irreducible representation of a Leibniz algebra can be obtained from irreducible representations of the semisimple Lie algebra from the Levi decomposition. We also prove that - in general - for (semi)simple…
To a finite dimensional representation of a complex Lie group $G$, an associative algebra of adjoint covariant polynomial maps from the direct sum of $m$ copies of the Lie algebra $\mathfrak{g}$ of $G$ into an algebra of complex matrices is…
We introduce a nonsymmetric, associative tensor product among representations of Cuntz algebras by using embeddings. We show the decomposition formulae of tensor products for permutative representations explicitly We apply decomposition…