Related papers: Tensor factorization and Spin construction for Kac…

In this thesis, we consider several aspects of over-extended and very-extended Kac-Moody algebras in relation with theories of gravity coupled to matter. In the first part, we focus on the occurrence of KM algebras in the cosmological…

This paper presents a natural generalisation of Saxl conjecture from a Lie-theoretical perspective, which is verified for the exceptional types. For classical types, progress is made using spin representations, revealing connections to…

We investigate the seven-sphere as a group-like manifold and its extension to a Kac-Moody-like algebra. Covariance properties and tensorial composition of spinors under $S^7$ are defined. The relation to Malcev algebras is established. The…

In physics, Lie groups represent the algebraic structure that describes symmetry transformations of a given system. Then, the descending Lie algebra of those groups are necessarily real. In most cases, the complexification of those Lie…

A semisimple algebraic tensor category over an algebraically closed field k of characteristic zero is the representation category of all finite dimensional twisted super representations of an affine reductive supergroup G over k. Such a…

We extend the definition of the Saito reflection functor of the Khovanov- Lauda-Rouquier algebras to symmetric Kac-Moody algebra case and prove that it defines a monoidal functor.

We provide an algorithm to calculate the invariant factors of the Shapovalov form on the standard $\Z$-lattice inside the basic representation of a Kac-Moody algebra of $ADE$ type, and give explicit formulae in some cases. The techniques…

$\pi$-systems are fundamental in the study of Kac-Moody Lie algebras since they arise naturally in the embedding problems. Dynkin introduced them first and showed how they also appear in the classification of semisimple subalgebras of a…

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…

We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices…

Automorphisms of finite order and real forms of "smooth" affine Kac-Moody algebras are studied, i.e. of 2-dimensional extensions of the algebra of smooth loops in a simple Lie algebra. It is shown that they can be parametrized by certain…

In the present article we introduce and study a class of topological reflection spaces that we call Kac-Moody symmetric spaces. These generalize Riemannian symmetric spaces of non-compact type. We observe that in a non-spherical Kac-Moody…

To each category C of modules of finite length over a complex simple Lie algebra g, closed under tensoring with finite dimensional modules, we associate and study a category Aff(C)_\kappa of smooth modules (in the sense of Kazhdan and…

Fock module realization for the unitary singleton representations of the $d-1$ dimensional conformal algebra $o(d-1,2)$, which correspond to the spaces of one-particle states of massless scalar and spinor in $d-1$ dimensions, is given. The…

Let $\mathfrak{g}$ be a symmetrizable Kac-Moody Lie algebra and let $\rho$ denote the sum of the fundamental weights. The irreducible highest weight representations $V(m\rho)$ occupy a distinguished position in representation theory due to…

We propose a generalization of the factorization method to the case when $\mathcal{G}$ is a finite dimensional Lie algebra such that $\mathcal{G}=\mathcal{G}_0\oplus M \oplus N$ (direct sum of vector spaces), where $\mathcal{G}_0$ is a…

Ian Grojnowski has developed a purely algebraic way to connect the representation theory of affine Hecke algebras at an (l+1)-th root of unity to the highest weight theory of the affine Kac-Moody algebra of type A_l^(1). The present article…

We study representations of the Loop Kac-Moody Lie algebra g \otimes A, where g is any Kac-Moody algebra and A is a ring of Laurent polynomials in n commuting variables. In particular, we study representations with finite dimensional weight…

In this paper we consider some Lie groups in complexified Clifford algebras. Using relations between operations of conjugation in Clifford algebras and matrix operations we prove isomorphisms between these groups and classical matrix groups…

In this paper we study complex representations of the factorpower $\fp(G,M)$ of a finite group $G$ acting on a finite set $M$. This includes the finite monoid $\FP$, which can be seen as a kind of a ``balanced'' generalization of the…