The coset and double-coset decompositions of the 420 subgroups of m(z)3(xyz)m(xy)1' (O(h)1') and the 236 subgroups of 6(z)/m(z)m(x)m(1)1' (D(6h)1') with respect to each of their subgroups are calculated along with additional mathematical properties of these groups.

Among other results, we rationally calculate the algebraic K-theory of any discrete cocompact subgroup of a Lie group G, where G is either O(n, 1), U(n, 1), Sp(n, 1), or F(4), in terms of the homology of the double coset space Gamma\G/K, where K is a maximal cocompact subgroup of G. We obtain the formula K(n)(ZGamma) [unk] [unk] congruent with [unk](i=0) (infinity)H(i)(Gamma\G/K; [unk](n-i)), w...

We study a type of generalized double coset operators which may change the characters modular forms. For any pair v1 and v2, we describe explicitly those mapping forms character to v2. give three applications, concerned with eta-quotients. first application, many pairs eta-quotients small weights levels, such that there are map one eta-quotient another. also find out these operators. second app...

Symmetry simplifications are introduced in configuration interaction (CI) by reducing the number of symmetry-allowed space types if there is degeneracy in some of the molecular orbitals by constructing the unique space types. A new symmetry group which we call the configuration symmetry group is defined and is shown to be expressible as a generalized wreath product group. Generating functions a...

Our concern will be mainly with the case where G/H is a homogeneous space of reductive type (Definition 5). If H is not compact, the action of a discrete subgroup Γ of G on G/H is not automatically properly discontinuous and the double coset Γ\G/H may be non-Hausdorff. This fact is the main difficulty in our problem. In fact, it may well happen that only finite subgroups of G can act properly d...

A bstract We formulate the stringy nonrelativistic limits of flat space and AdS 5 × S string as coset models, based on Bargmann extended Newton-Hooke algebras respectively. Our construction mimics typical relativistic one, but differs in several interesting ways. Using our formulation we give a Lax representation equations motion both models.