A Hopf algebraic approach to the theory of group branchings

Details A Hopf algebraic approach to the theory of group branchings A Hopf algebraic approach to the theory of group branchings

2005-08-17

arxiv.org/abs/math-ph/0508034v1

Physics

Mathematical Physics

13 pages, LaTeX, uses pstricks and osid Submitted to the B G Wybourne memorial conference proceedings

Scientific paper

We describe a Hopf algebraic approach to the Grothendieck ring of representations of subgroups $H_\pi$ of the general linear group GL(n) which stabilize a tensor of Young symmetry $\{\pi\}$. It turns out that the representation ring of the subgroup can be described as a Hopf algebra twist, with a 2-cocycle derived from the Cauchy kernel 2-cocycle using plethysms. Due to Schur-Weyl duality we also need to employ the coproduct of the inner multiplication. A detailed analysis including combinatorial proofs for our results can be found in math-ph/0505037. In this paper we focus on the Hopf algebraic treatment, and a more formal approach to representation rings and symmetric functions.

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