相关论文: Lie algebras, Fuchsian differential equations and …

We examine general aspects of parity functions arising in rational conformal field theories, as a result of Galois theoretic properties of modular transformations. We focus more specifically on parity functions associated with affine Lie…

We review some aspects of the free field approach to two-dimensional conformal field theories. Specifically, we discuss the construction of free field resolutions for the integrable highest weight modules of untwisted affine Kac-Moody…

We present a definition of the non-abelian generalisations of affine Toda theory related from the outset to vertex operator constructions of the corresponding Kac-Moody algebra $\gh$. Reuslts concerning conjugacy classes of the Weyl group…

We first review aspects of Kac Moody indefinite algebras with particular focus on their hyperbolic subset. Then we present two field theoretical systems where these structures appear as symmetries. The first deals with complete…

We develop a method to give presentations of quantized function algebras of complex reductive groups. In particular, we give presentations of quantized function algebras of automorphism groups of finite dimensional simple complex Lie…

Many integrable theories can be formulated universally in terms of Lie algebraic root systems. Well-studied are conformally invariant scalar field theories of Toda type and their massive versions, which can be expressed in terms of simple…

A Koszul duality-type correspondence between coderived categories of conilpotent differential graded Lie coalgebras and their Chevalley-Eilenberg differential graded algebras is established. This gives an interpretation of Lie coalgebra…

A concise review of the notions of elliptic functions, modular forms, and theta-functions is provided, devoting most of the paper to applications to Conformal Field Theory (CFT), introduced within the axiomatic framework of quantum field…

We construct the moduli spaces associated to the solutions of equations of motion (modulo gauge transformations) of the Poisson sigma model with target being an integrable Poisson manifold. The construction can be easily extended to a case…

On Lie algebras, we study commutative 2-cocycles, i.e., symmetric bilinear forms satisfying the usual cocycle equation. We note their relationship with antiderivations and compute them for some classes of Lie algebras, including…

Starting from noncommutative Fermi theory in two-dimensions, we construct a deformed Kac-Moody algebra between its vector and Chiral currents . The higher-order corrections to the deformed Kac-Moody algebra are explicitly calculated. We…

Let g be a Lie algebra over a field F of characteristic zero, let C be a certain tensor category of representations of g, and C-du a certain category of duals. In arXiv:math.AG/0409053 we associated to C and C-du by a Tannaka reconstruction…

The theory of Lie algebras can be categorified starting from a new notion of "2-vector space", which we define as an internal category in Vect. There is a 2-category 2Vect having these 2-vector spaces as objects, "linear functors" as…

We construct a set of non-rational conformal field theories that consist of deformations of Toda field theory for sl(n). Besides conformal invariance, the theories still enjoy a remnant infinite-dimensional affine symmetry. The case n=3 is…

Starting from an abelian rigid braided monoidal category C we define an abelian rigid monoidal category C_F which captures some aspects of perturbed conformal defects in two-dimensional conformal field theory. Namely, for V a rational…

The characters $\chi_\mu$ of nontwisted affine algebras at fixed level define in a natural way a representation $R$ of the modular group $SL_2(Z)$. The matrices in the image $R(SL_2(Z))$ are called the Kac-Peterson modular matrices, and…

We describe the resolution of field identification fixed points in coset conformal field theories in terms of representation spaces of the coset chiral algebra. A necessary ingredient from the representation theory of Kac Moody algebras is…

Duality relations between Lie algebras are a significant phenomenon in Lie algebra representation theory, with level-rank duality as a famous example. Level-rank dualities for affine Lie algebras of type $A^{(1)}$ were first discovered by…

In conformal field theory (CFT) on simply connected domains of the Riemann sphere, the natural conformal symmetries under self-maps are extended, in a certain way, to local symmetries under general conformal maps, and this is at the basis…

We provide new arguments to see topological Kac-Moody groups as generalized semisimple groups over local fields: they are products of topologically simple groups and their Iwahori subgroups are the normalizers of the pro-p Sylow subgroups.…