Representation Rings of Classical Groups and Hopf Algebras

Jian Zhou

doi:10.1142/s0129167x03001922

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Representation Rings of Classical Groups and Hopf Algebras

Jian Zhou

Year: 2003 Journal: International Journal of Mathematics Vol: 14 (05)Pages: 461-477 Publisher: World Scientific

DOI: 10.1142/s0129167x03001922

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Abstract

We prove a double coset formula for induced representations of compact Lie groups. We apply it to the representation rings of unitary and symplectic groups to obtain Hopf algebras. We also construct a Heisenberg algebra representation based on the restiction and induction of representations of unitary groups.

Keywords:

Mathematics Unitary state Unitary representation Hopf algebra Symplectic geometry Coset Pure mathematics Induced representation Restricted representation Classical group Algebra over a field (g,K)-module Irreducible representation Symplectic representation Unitary group Representation (politics) Symplectic group Representation theory of Hopf algebras Representation theory of SU Lie algebra Fundamental representation Lie group Algebra representation Discrete mathematics Division algebra Symplectic manifold Weight

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Algebraic structures and combinatorial models

Physical Sciences → Mathematics → Geometry and Topology

Advanced Topics in Algebra

Physical Sciences → Mathematics → Algebra and Number Theory

Advanced Algebra and Geometry

Physical Sciences → Mathematics → Mathematical Physics

Representation Rings of Classical Groups and Hopf Algebras

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