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Hopf algebras and characters of classical groups


King, RC and Fauser, B and Jarvis, PD, Hopf algebras and characters of classical groups, Journal of Physics: Conference Series, 5-12 September, 2007, Myczkowce, Poland, pp. 012030. ISSN 1742-6596 (2008) [Refereed Conference Paper]

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Copyright 2008 Institute of Physics

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DOI: doi:10.1088/1742-6596/104/1/012030


Schur functions provide an integral basis of the ring of symmetric functions. It is shown that this ring has a natural Hopf algebra structure by identifying the appropriate product, coproduct, unit, counit and antipode, and their properties. Characters of covariant tensor irreducible representations of the classical groups GL(n), O(n) and Sp(n) are then expressed in terms of Schur functions, and the Hopf algebra is exploited in the determination of group-subgroup branching rules and the decomposition of tensor products. The analysis is carried out in terms of n-independent, universal characters. The corresponding rings, CharGL, CharO and CharSp, of universal characters each have their own natural Hopf algebra structure. The appropriate product, coproduct, unit, counit and antipode are identified in each case.

Item Details

Item Type:Refereed Conference Paper
Research Division:Mathematical Sciences
Research Group:Mathematical physics
Research Field:Mathematical aspects of classical mechanics, quantum mechanics and quantum information theory
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Jarvis, PD (Dr Peter Jarvis)
ID Code:55487
Year Published:2008
Web of Science® Times Cited:2
Deposited By:Physics
Deposited On:2009-03-11
Last Modified:2009-06-10

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