A Hopf algebraic approach to the theory of group branchings
A Hopf algebraic approach to the theory of group branchings
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.
8323119015
75-86
Nicolaus Copernicus University Press
Fauser, B.
1fe23e36-240a-4331-9907-3eb3f4049cba
Jarvis, P.D.
99bb8f36-d7dd-4a55-b7e9-99bf6b3428c2
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
2006
Fauser, B.
1fe23e36-240a-4331-9907-3eb3f4049cba
Jarvis, P.D.
99bb8f36-d7dd-4a55-b7e9-99bf6b3428c2
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
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.
.
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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.
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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
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Date deposited: 28 Jul 2006
Last modified: 11 Dec 2021 15:52
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Contributors
Author:
B. Fauser
Author:
P.D. Jarvis
Author:
R.C. King
Editor:
R.C. King
Editor:
M. Bylicki
Editor:
J. Karwowski
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