Let G be the adjoint group of the simple real Lie algebra g , and let K C → Aut(p C ) be the complexified isotropy representation at the identity coset of the corresponding symmetric space. We classify the spherical nilpotent K C orbits in p C .

In this paper, we study the rationality of the Reidemeister zeta function of an endomorphism of a group extension. As an application, we give sufficient conditions for the rationality of the Reidemeister and the Nielsen zeta functions of selfmaps on an exponential solvmanifold or an infra-nilmanifold or the coset space of a compact connected Lie group by a finite subgroup.

The tensionless limit of gauged WZW models arises when the level of the underlying Kac-Moody algebra assumes its critical value, equal to the dual Coxeter number, in which case the central charge of the Virasoro algebra becomes infinite. We examine this limit from the world-sheet and target space viewpoint and show that gravity decouples naturally from the spectrum. Using the two-dimensional bl...

Coset models and their symmetry preserving branes are studied from a representation theoretic perspective, relating e.g. the horizontal branching spaces to a truncation of the space of bulk fields, and accounting for field identification. This allows us to describe the fuzzy geometry of the branes at finite level.

We prove that the dualization algebra of the symmetric space coset sigma model is a Lie algebra and we show that it generates an appropriate adjoint representation which enables the local integration of the field equations yielding the first-order ones.

An action for supersymmetric D0-branes in curved backgrounds is obtained by dimensional reduction of N=1 ten-dimensional supergravity coupled to super Yang-Mills system to 0+1 dimensions. The resultant action exhibits the coset-space symmetry SO(9,9+n) SO(9)×SO(9+n) ×U(1) where n = N−1 is the dimension of the SU(N) gauge group.

We present a simple derivation of the Ricci-flat Kähler metric and its Kähler potential on the canonical line bundle over arbitrary Kähler coset space equipped with the Kähler-Einstein metric. ∗ E-mail: [email protected] † E-mail: [email protected] ‡ E-mail: [email protected]

The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim σ-models, and they are integrable exhibiting a black-hole type metric in target space. We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups F ⊃ G ⊃ H . We show that for every symmetric space F/G, the generalized sine-Gordon models can be derived from the G/H WZW action, p...

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...