English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the zaia usage as premium feature

ZAIA

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the access of premium content as premium feature

Premium Content

Zendy Tools

Zendy Open

We begin by studying the irreducible complex representations of the "building block groups" of orders n 2 and n 3 , and how the representations for the composite groups are constructed from them. This of course also gives a complete set of inequivalent irreducible matrix representations for the generalized Clifford algebras corresponding to these groups. We apply these representation-theoretic results to determine the size of the maximal abelian subgroups of these groups, and to present a generalization of a result of Littlewood on maximal sets of anticommuting matrices. In the final section we consider an alternative generalization of the CLE-groups, in which we require a n = 1, but allow aiaj = ω k ajai for fixed k dividing n, where possibly k > 1. The irreducible complex representations of these groups are then calculated. These representations have been studied from the standpoint of projective representations of ( /n ) r in [S-I]. However we feel that the presentation given here is somewhat clearer. The results again are of interest to physicists in a number of applications (see [S-I], [Kw]).Throughout this paper the notation and conventions will follow those of [Sm1], [Sm2]. The results of [Sm 2] concerning the explicit decomposition of the groups will be used extensively here. The corresponding generalized Clifford algebras are studied in [Sm3].

Generalized Clifford-Littlewood-Eckmann groups II: Linear representations and applications