We study the properties of a future singularity encountered by a perfect fluid observer in tilting spatially homogeneous Bianchi cos-mologies. We derive the boost formulae for the Weyl tensor to establish that, for two observers that are asymptotically null with respect to each other, their respective Weyl parameters generally both tend to zero, constant, or infinity together. We examine three ...

A graph structure is deened on the Weyl groups. We show that these graphs are connected for Weyl groups of type An for n 4. 1. Introduction. We have deened a graph structure on Weyl groups through the root system associated with them. The planarity and the other properties of such graphs has been studied elsewhere (1] and 2]). The motivation for these graphs come from the method employed in pro...

We use the author's combinatorial theory of full heaps to categorify the action of a large class of Weyl groups on their root systems, and thus to give an elementary and uniform construction of a family of faithful permutation representations of Weyl groups. Examples include the standard representations of affine Weyl groups as permutations of Z and geometrical examples such as the realization ...

We use the author's combinatorial theory of full heaps to categorify the action of a large class of Weyl groups on their root systems, and thus to give an elementary and uniform construction of a family of faithful permutation representations of Weyl groups. Examples include the standard representations of affine Weyl groups as permutations of Z and geometrical examples such as the realization ...

We study the properties of a future singularity encountered by a perfect fluid observer in tilting spatially homogeneous Bianchi cos-mologies. We derive the boost formulae for the Weyl tensor to establish that, for two observers that are asymptotically null with respect to each other, their respective Weyl parameters generally both tend to zero, constant, or infinity together. We examine three ...

Local Weyl modules over two-dimensional currents with values in glr are deformed into spaces with bases related to parking functions. Using this construction we 1) reproof that dimension of the space of diagonal coinvariants is not less than the number of parking functions; 2) describe the limit of Weyl modules in terms of semi-infinite forms and find the limit of characters; 3) propose a lower...

Let G be a connected reductive group. To any irreducible G-variety one associates a certain linear group generated by reflections called the Weyl group. Weyl groups play an important role in the study of embeddings of homogeneous spaces. We establish algorithms for computing Weyl groups for homogeneous spaces and affine homogeneous vector bundles. For some special classes of G-varieties (affine...

Abstract We apply Weyl

We demonstrate the relation between the isospectral deformation and Rieffel’s deformation quantization by the action of R.

We discuss the procedure of Rieffel induction of representations in the framework of formal deformation quantization of Poisson manifolds. We focus on the central role played by algebraic notions of complete positivity.