Related papers: Ground state representations of loop algebras

Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for smooth (and generalized) connections is…

The purpose of this paper is to study representations of simple multiplicative Hom-Lie algebras. First, we provide a new proof using Killing form for characterization theorem of simple Hom-Lie algebras given by Chen and Han, then discuss…

Based on recent advancements in algebraic geometry, algebraic topology, and higher-categorical structures, we show how ground state degeneracies in closed stratified manifolds can be used for describing class ${\cal S}$ theories whose AGT…

We adapt methods from the theory of complex semisimple Lie algebras to develop a root theory for a class of simple $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded (color) Lie algebras, which we call basic. As an application, assuming that the…

The representation theory of symmetric Lie superalgebras and corresponding spherical functions are studied in relation with the theory of the deformed quantum Calogero-Moser systems. In the special case of symmetric pair g=gl(n,2m),…

It is proposed that instead of normal representations one should look at cocycles of group extensions valued in certain groups of unitary operators acting in a Hilbert space (e.g the Fock space of chiral fermions), when dealing with groups…

Let $f:V\times V\to F$ be a totally arbitrary bilinear form defined on a finite dimensional vector space $V$ over a a field $F$, and let $L(f)$ be the subalgebra of $\gl(V)$ of all skew-adjoint endomorphisms relative to $f$. Provided $F$ is…

Let $\mathfrak{g}$ be a real finite-dimensional Lie algebra equipped with a symmetric bilinear form $\langle\cdot,\cdot\rangle$. We assume that $\langle\cdot,\cdot\rangle $ is nil-invariant. This means that every nilpotent operator in the…

Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…

We present some recently discovered infinite dimensional Lie algebras that can be understood as extensions of the algebra Map(M,g) of maps from a compact p-dimensional manifold to some finite dimensional Lie algebra g. In the first part of…

The category of unital (unbounded) dg cocommutative coalgebras over a field of characteristic zero is provided with a structure of simplicial closed model category. This generalizes the model structure defined by Quillen in 1969 for…

We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level l projective unitary positive-energy representations of…

Let G be a real semisimple algebraic Lie group and H a real reductive algebraic subgroup. We describe the pairs (G,H) for which the representation of G in $L^2(G/H)$ is tempered. When G and H are complex Lie groups, the temperedness…

Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…

The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non- degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalised the LQG…

Recall the classical result that the cup product structure constants for the singular cohomology with integral coefficients of the Grassmannian of r-planes coincide with the Littlewood-Richardson tensor product structure constants for…

We give closed formulae for the q-characters of the fundamental representations of the quantum loop algebra of a classical Lie algebra in terms of a family of partitions satisfying some simple properties. We also give the multiplicities of…

In Lie sphere geometry, a cycle in $\RR^n$ is either a point or an oriented sphere or plane of codimension $1$, and it is represented by a point on a projective surface $\Omega\subset \PP^{n+2}$. The Lie product, a bilinear form on the…

We present the extension of the Lagrangian $loop$ representation in such a way to introduce matter fields. The partition function of lattice compact U(1) Gauge-Higgs model is expressed as a sum over closed as much as open surfaces. These…

We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint…