×

Matrix elements for indecomposable representations of complex su(2). (English) Zbl 0548.17005

A ”master” representation of the simple complex Lie algebra \(A_ 1\) on its universal enveloping algebra \(\Omega\) is constructed. Other representations are then determined on various subspaces, quotient spaces, quotient spaces of subspaces etc. This work generalises that of an earlier paper of the authors [J. Math. Phys. 19, 2009-2017 (1978; Zbl 0425.22023)]. Both finite and infinite dimensional irreducible representations are discussed as well as indecomposable representations. The methods used are entirely algebraic and in each case matrix elements are obtained in an explicit form.
Reviewer: R.C.King

MSC:

17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
22E70 Applications of Lie groups to the sciences; explicit representations
17B20 Simple, semisimple, reductive (super)algebras
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations

Citations:

Zbl 0425.22023
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.2307/1969129 · Zbl 0045.38801 · doi:10.2307/1969129
[2] DOI: 10.1016/0003-4916(66)90135-7 · Zbl 0144.23804 · doi:10.1016/0003-4916(66)90135-7
[3] DOI: 10.1063/1.522817 · doi:10.1063/1.522817
[4] DOI: 10.1063/1.1665687 · doi:10.1063/1.1665687
[5] DOI: 10.1063/1.1665687 · doi:10.1063/1.1665687
[6] DOI: 10.1063/1.523575 · Zbl 0425.22023 · doi:10.1063/1.523575
[7] DOI: 10.1063/1.524993 · doi:10.1063/1.524993
[8] DOI: 10.1063/1.524993 · doi:10.1063/1.524993
[9] Maillard J. M., C. R. Acad. Sci. Paris Ser. A 280 pp 73– (1975)
[10] Arnal D., Bull. Soc. Math. France 101 pp 381– (1973)
[11] DOI: 10.1063/1.522757 · Zbl 0308.17002 · doi:10.1063/1.522757
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.