In particular, the fact that ideas regarding Jacquet modules and the double coset method (regarding intertwining operators) can be developed in this generality is useful in applications. Since we are interested in such things as Jacquet modules, we more generally consider the notions of isotype and co-isotype. Spherical representations and admissibility, at the end, may seem mysterious at this ...

In symmetric groups, viewed as Coxeter groups, we show that the set of elements of minimal length in a double sided cell is the set of elements of maximal length in conjugated parabolic (i.e. Young) subgroups. We also give an interpretation of these sets with tableau, using the RobinsonSchensted correspondence. We show also that the set of elements of maximal length in a two sided cell is the s...

the existence of some geometrically imperfect members, like initial curvature in a double layer space structures with hundreds or thousands of members is almost inevitable. these imperfections give rise to loss of load bearing capacity of double layer space structures. to evaluate the effect of initial member imperfection on load bearing capacity of double layer space structures and their failu...

Let G be a connected, linear semisimple Lie group with Lie algebra g, and let KC → Aut(pC ) be the complexified isotropy representation at the identity coset of the corresponding symmetric space. The Kostant-Sekiguchi correspondence is a bijection between the nilpotent KC -orbits in pC and the nilpotent G-orbits in g. We show that this correspondence associates each spherical nilpotent KC -orbi...

Various exact two-dimensional conformal field theories with AdS2d+1 target space are constructed. These models can be solved using bosonization techniques and are examples of a more general novel type of coset construction. Some of them can be used to build perturbative superstring theories with AdS backgrounds, including AdS5.

The method of coset-space dimensional reduction is employed in order to proceed from a gauged E8 × E ′ 8 unified theory defined in 10 dimensions to 4 dimensions. The resulting theory comprises the Standard Model along with a strongly-interacting fermion sector which breaks the electroweak symmetry dynamically at the right scale. e-mail:[email protected] e-mail:[email protected]

We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the problem of classification of principal fibre bundles, which is important for the quantization of gauge theories. Some results for bundles over two-dimensional...

The idea behind the coset code construction (see [G.D. Forney, Coset Codes, IEEE Transactions on Information Theory, Part I: Introduction and Geometrical Classification, pp. 1123–1151; Part II: Binary lattices and related codes, pp. 1152–1187; F.R. Kschischang and S. Pasupathy, IEEE Transactions on Information Theory 38 (1992), 227–246.]) is to reduce the construction of sphere packings to erro...

Skew lattices are the most successful generalization of lattices to the noncommutative case to date. Roughly speaking, each skew lattice can be seen as a lattice of rectangular bands. A coset decomposition can be given to each pair of comparable maximal rectangular bands. The internal structure of skew lattices is revealed by their coset structure. In the present paper we study the coset struct...