Preprint 77/2005

A Hopf algebraic approach to the theory of group branchings

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

Contact the author: Please use for correspondence this email.
Submission date: 16. Aug. 2005
Pages: 15
published in: Symmetry, spectroscopy and SCHUR : proceedings of the Professor Brian G. Wybourne Commemorative Meeting, Torun, 12-14 June 2005 / R. C. King (ed.)
Torun : Nicolaus Copericus University Press, 2006. - P. 75 - 86 
MSC-Numbers: 05E05, 16W30, 20G10, 11E57
Keywords and phrases: group branchings, symmetric functions, plethysm,, hopf algebra, representation rings
Download full preprint: PDF (223 kB), PS ziped (248 kB)

HGL We describe a Hopf algebraic approach to the Grothendieck ring of representations of subgroups formula11 of the general linear group formula13 which stabilize a tensor of Young symmetry formula15. 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.

03.04.2017, 12:08