Related papers: Fusion bases for affine Lie algebras
The uniformity of the decomposition law, for a family F of Lie algebras which includes the exceptional Lie algebras, of the tensor powers ad^n of their adjoint representations ad is now well-known. This paper uses it to embark on the…
We give uniform formulas for the branching rules of level 1 modules over orthogonal affine Lie algebras for all conformal pairs associated to symmetric spaces. We also provide a combinatorial intepretation of these formulas in terms of…
We give a realization of the quantum affine Lie algebras $\uqa$ and $\uqc$ in terms of anyons defined on a one-dimensional chain (or on a two-dimensional lattice), the deformation parameter $q$ being related to the statistical parameter…
The homology of free Lie algebras with coefficients in tensor products of the adjoint representation working over Q contains important information on the homological properties of polynomial outer functors on free groups. The latter…
For the Lie algebras $g_n= \mathfrak{o}_{2n+1},\mathfrak{sp}_{2n},\mathfrak{o}_{2n}$ a simple construction of a base in an irreducible representation is given. The construction of this base uses the method of $Z$-invariants of Zhelobenko…
In this paper we will first introduce the notion of affine structures on a ringed space and then obtain several properties. Affine structures on a ringed space, arising mainly from complex analytical spaces of algebraic schemes over number…
This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras.
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…
In this paper we construct bases of standard (i.e. integrable highest weight) modules $L(\Lambda)$ for affine Lie algebra of type $B_2\sp{(1)}$ consisting of semi-infinite monomials. The main technical ingredient is a construction of…
We construct an integral PBW basis and an integral crystal basis of the quantum affine algebra of type A$_{2}^{(2)}$.
For all almost affine (hyperbolic) Lie superalgebras, the defining relations are computed in terms of their Chevalley generators.
In this article, we give an explicit formula for the universal weight function of the quantum twisted affine algebra $U_q(A_2^{(2)})$. The calculations use the technique of projecting products of Drinfeld currents onto the intersection of…
Fusion rules among irreducible modules of the free bosonic orbifold vertex operator algebra are completely determined.
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
For Lie algebras whose Poisson semi-center is a polynomial ring we give a bound for the sum of the degrees of the generating semi-invariants. This bound was previously known in many special cases.
In this paper, we explore natural connections among trigonometric Lie algebras, (general) affine Lie algebras, and vertex algebras. Among the main results, we obtain a realization of trigonometric Lie algebras as what were called the…
Restricted twisted Heisenberg Lie superalgebras are studied over an algebraically closed field F of characteristic p > 0. We determine the restricted structures and use the ordinary 1- and 2-cohomology spaces with trivial coefficients to…
A complete classification of the WZNW modular invariant partition functions is known for very few affine algebras and levels, the most significant being all levels of SU(2), and level 1 of all simple algebras. In this paper we solve the…
We study simply-laced simple affine Lie algebra bundles over complex surfaces X. Given any Kodaira curve C in X, we construct such a bundle over X. After deformations, it becomes trivial on every irreducible component of C provided that…
Polynomial relations for generators of $su(2)$ Lie algebra in arbitrary representations are found. They generalize usual relation for Pauli operators in spin 1/2 case and permit to construct modified Holstein-Primakoff transformations in…