In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not suffer this restriction and we present some examples of infinite double coset systems which can now easily be solved using our approach. Even when both enumerati...

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...

1. The statement of theorems. Let G be a connected complex Lie group and let B be a closed complex Lie subgroup in G. The left coset space G/B is a complex manifold, which will be called a complex coset space. We denote by Bo the identity connected component of B and U the normalizer of BoThe canonical projection p of G/B onto G/ U defines a holomorphic fibre bundle, and the complex Lie group U...

The problem of providing complete presentations reduction algebras associated to a pair Lie $$( \mathfrak{G} , \mathfrak{g} )$$ has previously been considered by Khoroshkin and Ogievetsky in the case diagonal algebra for $$\mathfrak{gl}(n)$$ . In this paper, we consider superalgebras \mathfrak{osp}(1|2) \times as double coset space having an associative $$ \mathrel{\scriptstyle\lozenge} -produc...

It is shown that the space of cohomology classes of the SU(1, 1)/U(1) coset at negative level k contains states of relevant conformal dimensions. These states correspond to the energy density operator of the associated nonlinear sigma model. We exhibit that there exists a subclass of relevant operators forming a closed fusion algebra. We make use of these operators to perform renormalizable per...

Let G=H be an irreducible globally hyperbolic semisimple symmetric space, and let S G be a subsemigroup containing H not isolated in S. We show that if S o 6 = then there are H-invariant minimal and maximal cones C min C max in the tangent space at the origin such that H exp C min S HZ K (a) exp C max. A double coset decomposition of the group G in terms of Cartan subspaces and the group H is p...

This is the author's second paper treating double coset problem for classical groups. Let G be an algebraic group over algebraically closed field K . The consists of classifying pairs H , J connected subgroups with finitely many ( ) -double cosets in critical setup occurs when reductive and a parabolic subgroup. Assume that group, simple maximal P k stabilizer totally singular -space. We show i...