Let G be a semisimple algebraic group over [Formula: see text]. For reduced word text] of the longest element in Weyl and dominant integral weight text], one can construct string polytope whose lattice points encode character irreducible representation The is singular general combinatorics polytopes heavily depends on choice In this paper, we study when present sufficient condition such that to...

This paper relates the boundary term in the Chern-Gauss-Bonnet formula on 4-manifolds M with the renormalized volume V , as defined in the AdS/CFT correspondence, for asymptotically hyperbolic Einstein metrics on M . In addition we compute and discuss the differential or variation dV of V , or equivalently the variation of the L norm of the Weyl curvature, on the space of such Einstein metrics....

We present a formal, algebraic treatment of Fedosov’s argument that the coordinate algebra of a symplectic manifold has a deformation quantization. His remarkable formulas are established in the context of affine symplectic algebras.

A strict quantization of a Poisson manifold P on a subset

In the framework of C-algebraic deformation quantization we propose a notion of deformation groupoid which could apply to known examples e.g. Connes’ tangent groupoid of a manifold, its generalisation by Landsman and Ramazan, Rieffel’s noncommutative torus, and even Landi’s noncommutative 4-sphere. We construct such groupoid for a wide class of T-spaces, that generalizes the one given for C by ...

Let G be a 1-connected, almost-simple Lie group over a local field and S a subsemigroup of G with non-empty interior. The action of the regular hyperbolic elements in the interior of S on the flag manifold G/P and on the associated Euclidean building allows us to prove that the invariant control set exists and is unique. We also provide a characterization of the set of transitivity of the contr...