PRODUCT SPLITTINGS FOR p-COMPACT GROUPS
نویسندگان
چکیده
Remark. If G is a compact Lie group with maximal torus TG and Weyl Group WG, the finitely generated free Z-module LG = π1TG has a natural action of WG and is called the dual weight lattice of G. The group G is simple in the usual sense if and only if the center of G is trivial and the action of WG on Q ⊗ LG gives an irreducible representation of WG over Q. From this point of view 1.3 is a direct analogue of 1.1.
منابع مشابه
Abstract structure of partial function $*$-algebras over semi-direct product of locally compact groups
This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism. Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...
متن کاملBracket Products on Locally Compact Abelian Groups
We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).
متن کاملA Compact Scheme for a Partial Integro-Differential Equation with Weakly Singular Kernel
Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...
متن کاملOn Non-compact Heegaard Splittings
A Heegaard splitting of an open 3-manifold is the partition of the manifold into two non-compact handlebodies which intersect on their common boundary. This paper proves several non-compact analogues of theorems about compact Heegaard splittings. The main theorem is: if N is a compact, connected, orientable 3-manifold with non-empty boundary, with no S components, and if M is obtained from N by...
متن کاملA tensor product approach to the abstract partial fourier transforms over semi-direct product groups
In this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the Fourier transform. As a consequence, we extend the fundamental theorems of Abelian Fourier transform to non-Abelian case.
متن کامل