Abstract
This paper reproduces the result of Elliot, namely that the irreducible finite dimensional representation of the Lie algebra su(3) of highest weight (m, n) is decomposed according to the embedding so(3) ⊂ su(3). First, a realisation (a representation in terms of vector fields) of the Lie algebra su(3) is constructed on a space of polynomials of three variables. The special polynomial basis of the representation space is given. In this basis, we find the highest weight vectors of the representation of the Lie subalgebra so(3) and in this way the representation space is decomposed to the direct sum of invariant subspaces. The process is illustrated by the example of the decomposition of the representation of highest weight (2, 2). As an additional result, the generating function of the decomposition is given.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
