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Hopf algebras and characters of classical groups
conference contribution
posted on 2023-05-23, 04:22 authored by King, RC, Fauser, B, Peter JarvisPeter JarvisSchur 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.
History
Publication title
Journal of Physics: Conference SeriesVolume
104Editors
T Lulek, A Wal and B LulekPagination
012030ISSN
1742-6596Department/School
School of Natural SciencesPublisher
IOP PublishingPlace of publication
United KingdomEvent title
Symmetry and Structural Properties of Condensed MatterEvent Venue
Myczkowce, PolandDate of Event (Start Date)
2007-09-05Date of Event (End Date)
2007-09-12Rights statement
Copyright © 2008 Institute of PhysicsRepository Status
- Restricted