A Method for the Computation of Clebsch-Gordan Coefficients
Year: 1991
Type: article
Abstract: Clebsch-Gordan series, Clebsch-Gordan coefficients Let G be a semisimple connected Lie group, g its Lie algebra, gC the complexification of g. A finite dimensional irreducible representation of G (of g, gC) with highest weight m will be denoted by [m]. Let be [m′] and [m′′] be two such representations with representation spaces V ′ and V ′ ′. In general, the tensor product [m′] ⊗ [m′′] is a direct sum of irreducible representations [mi] with the multiplicities ni: [m ′ ] ⊗ [m ′ ′ ] = ∑ ni[mi] i∈I (Clebsch-Gordan series). Furthermore, we will assume that for every irreducible representation [m] in the representation space V is given a basis {g(m, p1, p2,...) : p1, p2,...} described by parameters p1, p2,... which range over some intervals. This basis we shall call a canonical basis for [m] in the following. (We do not give an exact definition of the canonical basis here). In V ′ ⊗ V ′ ′ we have two distinguished bases: The product basis {g(m ′ , p ′ 1, p ′ 2,...) ⊗ g(m′ ′ , p ′′ 1, p′ ′ 2,...) : p ′ 1, p ′ 2,..., p′′
Source: Journal of Lie Theory
DOI: 10.5802/jolt.10
Author: H. Schlosser
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7140518778