Related papers: On the relation between integrability and infinite…
We argue that the Leutheusser-Liu procedure of isolating a von Neumann algebra in the $N = \infty$ limit of string theories, leads to the algebra of relativistic fermion fields on a half line for the $c = 1$ string theory. This is a Type…
Irreducible nonzero level modules with finite-dimensional weight spaces are studied for non-twisted affine Lie superalgebras. A complete classification is obtained for superalgebras A(m,n)^ and C(n)^. In other cases the classification…
We derive sufficient conditions under which the ``second'' Hamiltonian structure of a class of generalized KdV-hierarchies defines one of the classical $\cal W$-algebras obtained through Drinfel'd-Sokolov Hamiltonian reduction. These…
We construct a new family of infinite-dimensional quasi-graded Lie algebras on hyperelliptic curves. We show that constructed algebras possess infinite number of invariant functions and admit a decomposition into the direct sum of two…
We present a construction which associates an infinite sequence of Kac-Moody algebras, labeled by a positive integer n, to one single Jordan algebra. For n=1, this reduces to the well known Kantor-Koecher-Tits construction. Our…
This paper is devoted to the quantum integrable structure of Wess-Zumino-Novikov-Witten models, formed by an infinite number of commuting Integrals of Motion (IMs) in their current algebra. Focusing for simplicity on the SU(2) case, we…
We compare and generalise the various geometric constructions (due to Ringel, Lusztig, Schofield, Bozec, Davison...) of the unipotent generalised Kac-Moody algebra associated with an arbitrary quiver. These constructions are interconnected…
We discuss In\"on\"u-Wigner contractions of affine Kac-Moody algebras. We show that the Sugawara construction for the contracted affine algebra exists only for a fixed value of the level $k$, which is determined in terms of the dimension of…
By generalizing the Drinfeld-Sokolov reduction a large class of $W$ algebras can be constructed. We introduce 'finite' versions of these algebras by Poisson reducing Kirillov Poisson structures on simple Lie algebras. A closed and…
In this paper we shall prove that the subalgebra generated over the integers by the divided powers of the Drinfeld generators $x_r^{\pm}$ of the Kac-Moody algebra of type $A_2^{(2)}$ is an integral form (strictly smaller than Mitzman's (see…
It is shown that each linear operator on a separable Hilbert space which generates a finite type I von Neumann algebra has, up to unitary equivalence, a unique representation as a direct integral of inflations of mutually unitary…
In this paper we study the inter-relationship between the integrable KP hierarchy, nonlinear $\hat{W}_{\infty}$ algebra and conformal noncompact $SL(2,R)/U(1)$ coset model at the classical level. We first derive explicitly the Possion…
We study the irreducible unitary highest weight representations, which are obtained from free field realizations, of $W$ infinity algebras ($W_{\infty}$, $W_{1+\infty}$, $W_{\infty}^{1,1}$, $W_{\infty}^M$, $W_{1+\infty}^N$,…
In the article at hand, we sketch how, by utilizing nilpotency to its fullest extent (Engel, Super Engel) while using methods from the theory of universal enveloping algebras, a complete description of the indecomposable representations may…
We present a new family of IR dualities in three space-time dimensions with eight supercharges. In contrast to 3d mirror symmetry, these dualities map Coulomb branches to Coulomb branches and Higgs branches to Higgs branches in the deep IR.…
The deformations of an infinite dimensional algebra may be controlled not just by its own cohomology but by that of an associated diagram of algebras, since an infinite dimensional algebra may be absolutely rigid in the classical…
In this study the notion of particular integrability in Classical Mechanics, introduced in [J. Phys. A: Math. Theor. 46 025203, 2013], is revisited within the formalism of symplectic geometry. A particular integral $\cal I$ is a function…
We consider the maximal central extension of the supertranslation algebra in d=4 and 3, which includes tensor central charges associated to topological defects such as domain walls (membranes) and strings. We show that for all N-extended…
Many $W$-algebras (e.g. the $W_N$ algebras) are consistent for all values of the central charge except for a discrete set of exceptional values. We show that such algebras can be contracted to new consistent degenerate algebras at these…
We study confining strings in massive adjoint two-dimensional chromodynamics. Off-shell, as a consequence of zigzag formation, the resulting worldsheet theory provides a non-trivial dynamical realization of infinite quon statistics. Taking…