Let g be a semisimple Lie algebra over the field of real numbers. G group with g. The Weyl respect to Cartan subalgebra h is defined as W(G,h)=NG(h)/ZG(h). We describe an explicit construction W(G,h) for groups that arise set points connected algebraic groups. show this also gives when adjoint This algorithm important classification regular subalgebras, carrier algebras, and nilpotent orbits as...

We generalize Conway-Sloane's constructions of the Leech lattice from Niemeier lattices using Lorentzian to holomorphic vertex operator algebras (VOA) central charge 24. It provides a tool for analyzing structures and relations among VOAs related by orbifold construction. In particular, we are able get some useful information about certain subVOAs associated with Cartan subalgebra weight one Li...

The analog of the principal SO(3) subalgebra of a finite dimensional simple Lie algebra can be defined for any hyperbolic Kac Moody algebra g(A) associated with a symmetrizable Cartan matrix A, and coincides with the non-compact algebra SO(1, 2). We exhibit the decomposition of g(A) into representations of SO(1, 2); with the exception of the adjoint SO(1, 2) algebra itself, all of these represe...

Conformal blocks for the WZW model on tori can be represented by vector valued Weyl anti-symmetric theta functions on the Cartan subalgebra satisfying vanishing conditions on root hyperplanes. We introduce a quantum version of these vanishing conditions in the sl2 case. They are compatible with the qKZB equations and are obeyed by the hypergeometric solutions as well as by their critical level ...

(identical representation). The even part G0 is characterized by the condition a0i = ai0 = 0 for i = 1, . . . , n. G0 is isomorphic to gl(n). We choose the Cartan subalgebra H as the set of diagonal matrices of G and G0 resp. Let eij be denote the (n+ 1)× (n+ 1)-matrix with 1 at the place (i, j) and 0 everywhere (i, j = 0, . . . , n) . Then we get by h1 = e00 + e11 , hi = ei−1,i−1 − eii (i = 2,...

In 1967, when Kadison and Ringrose began the development of continuous cohomology theory for operator algebras, they conjectured that the cohomology groups Hn(M, M), n >/= 1, for a von Neumann algebra M, should all be zero. This conjecture, which has important structural implications for von Neumann algebras, has been solved affirmatively in the type I, IIinfinity, and III cases, leaving open o...

We consider asymptotically flat static spherically symmetric black hole solutions in SU(N) Einstein-Yang-Mills theory. Embedding the N -dimensional representation of su(2) in su(N), the purely magnetic gauge field ansatz contains N − 1 functions. When one or more of these gauge field functions are identically zero, magnetically charged EYM black hole solutions emerge, consisting of a neutral an...

Let g denote a reductive Lie algebra over an algebraically closed field of characteristic zero, and let I) denote a Cartan subalgebra of g. In this paper we study finitely generated g-modules that decompose into direct sums of finite dimensional l)-weight spaces. We show that the classification of irreducible modules in this category can be reduced to the classification of a certain class of ir...

In [1], the wave functions of quantum trigonometric n-particle Ruijsenaars model are defined as matrix elements of operators of representations of Cartan subalgebra between vectors invariant with respect to q-deformation U ′ q(son) of Lie algebra so(n). It was shown there, that the wave functions defined in such a way are simultaneous eigenfunctions of commuting set of Macdonald–Ruijsenaars dif...

The group of area preserving diffeomorphisms of the annulus acts on its Lie algebra, the globally Hamiltonian vectorfields on the annulus. We consider a certain Hilbert space completion of this group (thinking of it as a group of unitary operators induced by the diffeomorphisms), and prove that the projection of an adjoint orbit onto a "Cartan" subalgebra isomorphic to Lz([0, 1]) is an infinite...