๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Diagram approach to group algebraic methods

โœ Scribed by R. J. Black; G. E. Stedman

Publisher
John Wiley and Sons
Year
1982
Tongue
English
Weight
435 KB
Volume
21
Category
Article
ISSN
0020-7608

No coin nor oath required. For personal study only.

โœฆ Synopsis

Abstract

Class sum theory, the duality with IRREP methods and tensor operators in the group algebra are discussed by generalizing the diagrammatic approach of conventional IRREP theory to include group label manipulation. Concepts such as invariant nodes and Jucysโ€“Levinsonโ€“Vanagas reduction theorems generalize straightforwardly. The results are capable of unique simplification for certain nodes, when the group rearrangement theorem is useable or when a class sum is performed. A duality transformation (between IRREPโ€“partner and classโ€“element labels) emerges as an important concept.

๐Ÿ“œ SIMILAR VOLUMES

An Algebraic Approach to Convolutions an
An Algebraic Approach to Convolutions and Transform Methods
โœ Luis Verde-Star ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 255 KB

We show that the Hopf algebra dual of the polynomials in one variable appears often in analysis, but under different disguises that include proper rational functions, exponential polynomials, shift invariant operators, Taylor functionals, and linearly recurrent sequences. The isomorphisms from the p

Diagram approach to character formulas f
Diagram approach to character formulas for finite and compact groups
โœ M. Kibler; E. Elbaz ๐Ÿ“‚ Article ๐Ÿ“… 1979 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 965 KB

## Abstract Some basic relations for the representation theory and the Wignerโ€“Racah algebra of a finite or compact continuous group are discussed and transcribed in terms of diagrams. Special emphasis is placed on the case of a simply reducible group and all the diagrams are applicable to __SU__~2~