Related papers: Type A fusion rules from elementary group theory

The algebra of strongly regular functions F[G_m] on a symmetrizable minimal Kac-Moody group G_m over a field F of characteristic zero has been introduced by V. Kac and D. Peterson as a coordinate ring of the minimal Kac-Moody group. We…

Let $G_k$ be a connected reductive group over an algebraically closed field $k$ of char $\neq 2$. Let $\theta_k$ be an algebraic group involution of $G_k$ and denote the fixed point subgroup by $K_k$. We construct an integral model for the…

We name an indecomposable symmetrizable generalized Cartan matrix $A$ and the corresponding Kac--Moody Lie algebra ${\goth g} ^\prime (A)$ {\it of the arithmetic type} if for any $\beta \in Q$ with $(\beta | \beta)<0$ there exist $n(\beta…

In this paper we determine the fusion rules of the logarithmic ${\calW}_{p,q}$ triplet theory and construct the Grothendieck group with subgroups for which consistent product structures can be defined. The fusion rules are then used to…

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…

Let $L$ be an even (positive definite) lattice and $g\in O(L)$. In this article, we prove that the orbifold vertex operator algebra $V_{L}^{\hat{g}}$ has group-like fusion if and only if $g$ acts trivially on the discriminant group…

To any symmetry of the Cartan matrix of a Generalized Kac-Moody (GKM) algebra we associate a family of automorphisms of the algebra which act in a natural way on the modules of the GKM algebra. We introduce the twining character of a module…

We provide evidence for the existence of a family of generalized Kac-Moody(GKM) superalgebras, G_N, whose Weyl-Kac-Borcherds denominator formula gives rise to a genus-two modular form at level N, Delta_{k/2}(Z), for (N,k)=(1,10), (2,6),…

The finite ring Z_k = Z(+,.) mod p^k of residue arithmetic with odd prime power modulus is analysed. The cyclic group of units G_k in Z_k(.) has order (p-1)p^{k-1}, implying product structure G_k = A_k B_k. Here core A_k of order p-1 is an…

The group $G = GL_r(k) \times (k^\times)^n$ acts on $\mathbf{A}^{r \times n}$, the space of $r$-by-$n$ matrices: $GL_r(k)$ acts by row operations and $(k^\times)^n$ scales columns. A matrix orbit closure is the Zariski closure of a point…

We show that the Hopf link invariants for an appropriate set of finite dimensional representations of $ U_q SL(2)$ are identical, up to overall normalisation, to the modular S matrix of Kac and Wakimoto for rational $k$ $\widehat {sl(2)}$…

Let $V$ be a simple, rational, $C_{2}$-cofinite vertex operator algebra of CFT type, and let $k$ be a positive integer. In this paper, we determine the fusion products of twisted modules for $V^{\otimes k}$ and $G = \left\langle g…

We show that, for a sheet or a Lusztig stratum S containing spherical conjugacy classes in a connected reductive algebraic group G over an algebraically closed field in good characteristic, the orbit space S/G is isomorphic to the quotient…

By a generalized Tannaka-Krein reconstruction we associate to the admissible representations of the category O of a Kac-Moody algebra, and its category of admissible duals a monoid with a coordinate ring. The Kac-Moody group is the Zariski…

We construct modular categories from Hecke algebras at roots of unity. For a special choice of the framing parameter, we recover the Reshetikhin-Turaev invariants of closed 3-manifolds constructed from the quantum groups U_q sl(N) by…

The natural representation of the quantized affine algebra of type A can be defined via the deformed Fock space by Misra and Miwa. This relates the classes of Weyl modules for a type A quantum group at a root of unity to the action of the…

The main result is that the category of ordinary modules of an affine vertex operator algebra of a simply laced Lie algebra at admissible level is rigid and thus a braided fusion category. If the level satisfies a certain coprime property…

The $K$-groups of the crossed product of the rotation C*-algebra $A_\theta$ by free and amalgamated products of the cyclic groups $\mathbb Z_n$, for $n=2,3,4,6$, are calculated. The actions here arise from the canonical actions of these…

Let $\FRAK{g}$ be a classical simple Lie superalgebra. To every nilpotent orbit $\cal O$ in $\FRAK{g}_0$ we associate a Clifford algebra over the field of rational functions on $\cal O$. We find the rank, $k(\cal O)$ of the bilinear form…

Axial algebras are commutative algebras generated by idempotents; they generalise associative algebras by allowing the idempotents to have additional eigenvectors, controlled by fusion rules. If the fusion rules are $\mathbb{Z}/2$-graded,…