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A Hopf algebraic approach to the theory of group branchings

Fauser, B., Jarvis, P.D. and King, R.C. (2006) A Hopf algebraic approach to the theory of group branchings. King, R.C., Bylicki, M. and Karwowski, J. (eds.) In Symmetry, Spectroscopy and SCHUR, Proceedings of Prof B.G, Wybourne Commemorative Meeting, Toru? Nicolaus Copernicus University Press. pp. 75-86 .

Record type: Conference or Workshop Item (Paper)

Abstract

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.

Published date: 2006
Venue - Dates: Professor Brian G. Wybourne Commemorative Meeting, Toruń, Poland, 2005-06-11 - 2005-06-13

Identifiers

Local EPrints ID: 41205
URI: http://eprints.soton.ac.uk/id/eprint/41205
ISBN: 8323119015
PURE UUID: 9a21552d-174f-40e3-b801-fe11c3a60b93

Catalogue record

Date deposited: 28 Jul 2006

Contributors

Author: B. Fauser
Author: P.D. Jarvis
Author: R.C. King
Editor: R.C. King
Editor: M. Bylicki
Editor: J. Karwowski