Higher-Dimensional Representations of SL2 and its Real Forms Via Plücker Embedding

The paper provides a geometric perspective on the inclusion map sl 2 ≅ so 3 ⊂ so n realized via the Plücker embedding. It relates higher-dimensional representations of the complex Lie group SO 3 and its real forms in terms of SO ( n ) and SO ( p , q ) transformations to different subspaces described...

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Bibliographic Details
Published in:Advances in applied Clifford algebras 2017-09, Vol.27 (3), p.2375-2392
Main Author: Brezov, Danail S.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Theoretical
Online Access:Get full text
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Summary:The paper provides a geometric perspective on the inclusion map sl 2 ≅ so 3 ⊂ so n realized via the Plücker embedding. It relates higher-dimensional representations of the complex Lie group SO 3 and its real forms in terms of SO ( n ) and SO ( p , q ) transformations to different subspaces described by means of the well-known double fibrations used in twistor theory. Moreover, explicit matrix realizations and various factorization techniques, such as Euler and Wigner decompositions, are constructed in this generalized setting. Examples are provided for n = 3 , 4 and 5 in the context of special relativity, classical and quantum mechanics.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-017-0765-3