Hopf algebras and characters of classical groups

Details Hopf algebras and characters of classical groups Hopf algebras and characters of classical groups

2007-10-14

arxiv.org/abs/0710.2648v1

Mathematics

Representation Theory

9 pages. Uses jpconf.cls and jpconf11.clo. Presented by RCK at SSPCM'07, Myczkowce, Poland, Sept 2007

Scientific paper

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.

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