A new set of tableaux indexing the weights of the irreducible representations of SO(2n + 1) is presented. These tableaux are used to produce an insertion scheme which gives a combinatorial description of the decomposition of the kth tensor power of the natural action of SO(2n + I ) into irreducibles. In particular, the multiplicities in this decomposition are described explicitly. C 1990 Academ...

1 Linear Equation Systems in the Numerical Solution of PDE’s 3 1.1 Examples of PDE’s . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Weak Formulation of Poisson’s Equation . . . . . . . . . . . . 6 1.3 Finite-Difference-Discretization of Poisson’s Equation . . . . . 7 1.4 FD Discretization for Convection-Diffusion . . . . . . . . . . 8 1.5 Irreducible and Diagonal Dominant Matrices . . . ...

Certainly the case of manifolds is the most interesting and most complicated. The main aim of this paper is to show that Conjecture I is not absolutely groundless. First our results deal with reflection orbifolds. In this case we will prove Conjecture 1 and find that R(Tq(M), 4) is a smooth manifold of dimension ( f -4 ) , where f is the number of "faces" of the reflection orbifold (Theorem 1)....

is a homomorphism of classical matrix Lie groups. The lefthand group consists of 2 × 2 complex matrices with determinant 1. The righthand group consists of 4× 4 real matrices with determinant 1 which preserve some fixed real quadratic form Q of signature (1, 3). This map is alternately called the spinor map and variations. The image of this map is the identity component of SO1,3(R), denoted SO1...