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Hopf algebras, distributive (Laplace) pairings and hash products: a unified approach to tensor product decompositions of group characters

Citation

Fauser, B and Jarvis, P and King, RC, Hopf algebras, distributive (Laplace) pairings and hash products: a unified approach to tensor product decompositions of group characters, Journal of Physics A: Mathematical and Theoretical, 47, (20) pp. 1-45. ISSN 1751-8113 (2014) [Refereed Article]

Copyright Statement

Copyright 2014 IOP Publishing Ltd

DOI: doi:10.1088/1751-8113/47/20/205201

Abstract

We show for bicommutative graded connected Hopf algebras that a certain distributive (Laplace) subgroup of the convolution monoid of 2-cochains parameterizes certain well behaved Hopf algebra deformations. Using the Laplace group, or its Frobenius subgroup, we define higher derived hash products, and develop a general theory to study their main properties. Applying our results to the (universal) bicommutative graded connected Hopf algebra of symmetric functions, we show that classical tensor product and character decompositions, such as those for the general linear group, mixed co- and contravariant or rational characters, orthogonal and symplectic group characters, Thibon and reduced symmetric group characters, are special cases of higher derived hash products. In the appendix we discuss a relation to formal group laws.

Item Details

Item Type:Refereed Article
Keywords:group representation theory, character theory, classical groups, Hopf algebra deformation theory
Research Division:Mathematical Sciences
Research Group:Mathematical Physics
Research Field:Mathematical Aspects of Classical Mechanics, Quantum Mechanics and Quantum Information Theory
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Jarvis, P (Dr Peter Jarvis)
ID Code:100318
Year Published:2014
Web of Science® Times Cited:2
Deposited By:Research Division
Deposited On:2015-05-11
Last Modified:2015-08-27
Downloads:0

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