Related papers: Fusion ring revisited
Twisted homomorphisms of bialgebras are bialgebra homomorphisms from the first into Drinfeld twistings of the second. They possess a composition operation extending composition of bialgebra homomorphisms. Gauge transformations of twists,…
We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety $X$, with first page built out of topological invariants associated to strata of any fixed normal crossings compactification…
This paper continues our investigation of a class of generalized quantum groups. The "standard" R-matrix was shown to be the unique solution of a very simple, linear recursion relation and the classical limit was obtained in the case of…
We construct holomorphic loop groups and their associated affine Kac-Moody groups and prove that they are tame Fr\'echet manifolds. These results form the functional analytic basis for the theory of affine Kac-Moody symmetric spaces,…
The infinite series of logarithmic minimal models LM(1,p) is considered in the W-extended picture where they are denoted by WLM(1,p). As in the rational models, the fusion algebra of WLM(1,p) is described by a simple graph fusion algebra.…
In this paper, by using the Lakshmibai-Seshadri paths, we give the branching rule for representations of affine Kac-Moody algebras to their winding subalgebras. As a corollary, we can describe branching multiplicities in the language of…
This article classifies the Vogan diagram of the affine untwisted Kac Moody superalgebras.
We investigate a class of Kac-Moody algebras previously not considered. We refer to them as n-extended Lorentzian Kac-Moody algebras defined by their Dynkin diagrams through the connection of an $A_n$ Dynkin diagram to the node…
A Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras and arbitrary subsets of the set of simple roots is proven. Moreover, quantum group analogs of the Bernstein-Gelfand-Gelfand resolution for symmetrizable Kac-Moody…
Given a simple finite-dimensional Lie algebra and an automorphism of finite order, one defines the notion of a twisted toroidal Lie algebra. In this paper, we construct representations of twisted toroidal Lie algebras from twisted modules…
In this paper we give a geometric construction of Cherednik's double affine Hecke algebra. We construct the algebra as the equivariant $K$-theory of the Lagrangian subvariety of the cotangent variety of the square of the flag variety of…
Recently, a class of interaction round the face (IRF) solvable lattice models were introduced, based on any rational conformal field theory (RCFT). We investigate here the connection between the general solvable IRF models and the fusion…
In the present note we suggest an affinization of a theorem by Kostrikin et.al. about the decomposition of some complex simple Lie algebras ${\cal G}$ into the algebraic sum of pairwise orthogonal Cartan subalgebras. We point out that the…
Following the definition of a root basis of an affine root system, we define a base of the root system of an affine Lie superalgebra to be a linearly independent subset $B$ of its root system such that each root can be written as a linear…
Let $X$ be a complex manifold, $\pi: E \rightarrow X$ a locally trivial holomorphic fibration with fiber $F$, and $\mathfrak{g}$ a Lie algebra with an invariant symmetric form. We associate to this data a holomorphic prefactorization…
We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.
In this paper we discuss the "Factorization phenomenon" which occurs when a representation of a Lie algebra is restricted to a subalgebra, and the result factors into a tensor product of smaller representations of the subalgebra. We analyze…
This paper introduces calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The primary technique is to provide indexing sets for controlling the…
In this note, we describe two analogues of the Verlinde formula for modular categories in a twisted setting. The classical Verlinde formula for a modular category $\mathscr{C}$ describes the fusion coefficients of $\mathscr{C}$ in terms of…
Twisted complex $K$-theory can be defined for a space $X$ equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C$^*$-algebras. Up to equivalence, the twisting corresponds to an element of $H^3(X;\Z)$. We…