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MiS Preprint
77/2005

A Hopf algebraic approach to the theory of group branchings

Bertfried Fauser, Peter D. Jarvis and Ronald C. King

Abstract

We describe a Hopf algebraic approach to the Grothendieck ring of representations of subgroups $\sf{H}_\pi$ of the general linear group $\sf{GL}(n)$ 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. In this paper we focus on the Hopf algebraic treatment, and a more formal approach to representation rings and symmetric functions.

Received:
Aug 16, 2005
Published:
Aug 16, 2005
MSC Codes:
05E05, 16W30, 20G10, 11E57
Keywords:
group branchings, symmetric functions, plethysm, hopf algebra, representation rings

Related publications

inBook
2006 Repository Open Access
Bertfried Fauser, Peter D. Jarvis and Ronald C. King

A Hopf algebraic approach to the theory of group branchings

In: Symmetry, spectroscopy and SCHUR : proceedings of the Professor Brian G. Wybourne Commemorative Meeting, Torun, 12-14 June 2005 / Ronald C. King (ed.)
Torun : Nicolaus Copericus University Press, 2006. - pp. 75-86