Principal realization of the Yangian Y(gl(n))

Journal Article · Thu Jan 15 04:00:00 EST 2009 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3050319· OSTI ID:21175902

Chengming, Bai ^[1]; Molin, Ge ^[2]; Naihuan, Jing ^[3]

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1. Chern Institute of Mathematics and LPMC, Nankai University, Tanjin 300071 (China)
2. Chern Institute of Mathematics, Nankai University, Tanjin 300071 (China)
3. Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205 (United States) and School of Sciences, South China University of Technology, Guangzhou 510640 (China)

Motivated to simplify the structure of tensor representations we give a new set of generators for the Yangian Y(sl(n)) using the principal realization in simple Lie algebras. The isomorphism between our new basis and the standard Cartan-Weyl basis is also given. We show by example that the principal basis simplifies the Yangian action significantly in the tensor product of the fundamental representation and its dual.

• OSTI ID: 21175902
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 1 Vol. 50; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
LIE GROUPS
MATHEMATICAL OPERATORS
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
TENSORS