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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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