Related papers: Fusion ring revisited

The fusion rings associated to affine Kac-Moody algebras appear in several different contexts in math and mathematical physics. In this paper we find all automorphisms of all affine fusion rings, or equivalently the symmetries of the…

We classify regular subalgebras of affine Kac-Moody algebras in terms of their root systems. In the process, we establish that a root system of a subalgebra is always an intersection of the root system of the algebra with a sublattice of…

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…

For any normal commutative Hopf subalgebra $K=k^G$ of a semisimple Hopf algebra we describe the ring inside $kG$ obtained by the restriction of $H$-modules. If $G=\Z_p$ this ring determines a fusion ring and we give a complete description…

For a rational and $C_2$-cofinite vertex operator algebra $V$ with an automorphism group $G$ of prime order, the fusion rules for twisted $V$-modules are studied, a twisted Verlinde formula which relates fusion rules for $g$-twisted modules…

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…

Let g be a semi-simple Lie algebra, and let g^ be the corresponding affine Kac-Moody algebra. Consider the category of g^-modules at the critical level, on which the action of the Iwahori subalgebra integrates to algebraic action of the…

These lecture notes are a brief introduction to Wess-Zumino-Witten models, and their current algebras, the affine Kac-Moody algebras. After reviewing the general background, we focus on the application of representation theory to the…

We develop a new method for obtaining branching rules for affine Kac-Moody Lie algebras at negative integer levels. This method uses fusion rules for vertex operator algebras of affine type. We prove that an infinite family of ordinary…

We construct certain Steinberg groups associated to extended affine Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame extended affine Lie…

We show how the fusion rules for an affine Kac-Moody Lie algebra g of type A_{n-1}, n = 2 or 3, for all positive integral level k, can be obtained from elementary group theory. The orbits of the kth symmetric group, S_k, acting on k-tuples…

We develop general foundations of topological algebra over a linearly topologized ring k in a format applicable to both formal schemes and analytic adic spaces. We are especially interested in determining exact closed tensor categories of…

We study Lusztig's t-analog of weight multiplicities associated to level one representations of twisted affine Kac-Moody algebras. An explicit closed form expression is obtained for the corresponding t-string function using constant term…

We interpret and develop a theory of loop algebras as torsors (principal homogeneous spaces) over Laurent polynomial rings . As an application, we recover Kac's realization of affine Kac-Moody Lie algebras.

This paper is about the orbifold theory of affine and parafermion vertex operator algebras. It is known that the parafermion vertex operator algebra $K(sl_2,k)$ associated to the integrable highest weight modules for the affine Kac-Moody…

We define the formal affine Demazure algebra and formal affine Hecke algebra associated to a Kac-Moody root system. We prove the structure theorems of these algebras, hence, extending several result and construction (presentation in terms…

We use the fusion construction in the twisted quantum affine algebras to obtain a unified method to deform the wedge product for classical Lie algebras. As a byproduct we uniformly realize all non-spin fundamental modules for quantized…

Let k be a commutative ring. We find and characterize a new family of twisted planes (i. e. associative unitary k-algebra structures on the k-module k[X,Y], having k[X] and and k[Y] as subalgebras).Similar results are obtained for the…

Invariant affine reflection algebras are the last and the most general known extension of affine Kac-Moody Lie algebras, introduced in recent years. We develop a method known as "affinization" to the class of invariant affine reflection…

We report on recent work concerning a new type of generalised Kac-Moody algebras based on the spaces of differentiable mappings from compact manifolds or homogeneous spaces onto compact Lie groups.