We characterize topological spaces which are coset of (separable) metrizable groups and complete (Polish) groups. Moreover, it is shown that for a $G$-space $X$ with $d$-open action there group $H$ weight cardin

2 Local theory 3 2.1 The endomorphism μ of V0(n) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Double coset representatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 The matrix of μ at level p2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 Eigenvalues of μ at level p2 for Iwahori-spherical representations . . . . . . . . . 17 2.5 Pr...

In this paper we prove that two Cartan subspaces of a semisimple symmetric pair (g, τ) are conjugate under G = Int(g) if and only if they are conjugate under (Gτ )0. Moreover we derive a double coset decomposition for G, which improves the results of Oshima and Matsuki.

We construct new algorithms from scratch, which use the fourth order cumulant of stochastic variables for the cost function. The multiplicative updating rule here constructed is natural from the homogeneous nature of the Lie group and has numerous merits for the rigorous treatment of the dynamics. As one consequence, the second order convergence is shown. For the cost function, functions invari...

We study the dimensional reduction of the N = 1, ten-dimensional Heterotic Supergravity to four dimensions, at leading order in α′, when the internal space is a coset manifold. Then we apply the formalism using as internal manifolds all possible six-dimensional nonsymmetric coset spaces, namely G2/SU(3), Sp4/(SU(2)× U(1))non−max and SU(3)/U(1)× U(1), which moreover are nearly-Kähler manifolds a...

A new framework for multivariate optimization by criteria invariant under componentwise scaling is constructed. These problems are naturally considered as problems on the coset . We show that there is a duality between the optimization flow on this coset and the dynamics of quantum lattice with inner degrees of freedom. Then we propose a new algorithm for optimization problems on this coset nam...

We explain how one can construct a class of discrete hypergroups which are non-unimodular. They arise as double coset hypergroups induced by the transitive action of a non-unimodular group of permutations on an innnite set. A concrete example is given in terms of the aane group of a homogeneous tree.

We examine the vacua of scalar potential effective 4-d action, obtained after dimensional reduction 10-d N = 1 $\mathcal {N}=1$ heterotic supergravity coupled to an Yang-Mills sector. The (Coset Space) takes place over three 6-d nearly-Kähler manifolds, namely homogeneous non-symmetric coset spaces, G 2 / S U ( 3 ) $G_2/SU(3)$ , p 4 × $Sp_4/SU(2)\times U(1)$ and $SU(3)/U(1)\times . current work...

We show that the double of the nontrivially associated tensor category constructed from left coset representatives of a subgroup of a finite group X is a modular category. Also we give a definition of the character of an object in this category as an element of a braided Hopf algebra in the category. This definition is shown to be adjoint invariant and multiplicative on tensor products. A detai...