2014
DOI: 10.1088/1751-8113/47/20/205201
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Hopf algebras, distributive (Laplace) pairings and hash products: a unified approach to tensor product decompositions of group characters

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 charac… Show more

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Cited by 4 publications
(3 citation statements)
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“…The present paper gives further development of the algebraic-combinatorial context for the description of the general classes of symmetric functions of π-type, introduced in our previous papers [8,9,10]. Specifically, further to the previously-derived π-type 'plethystic' vertex operators given as the algebraic tools for deriving the π-type symmetric functions as modal products, we have identified in this work the dual counterparts of these objects.…”
Section: Conclusion and Related Workmentioning
confidence: 85%
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“…The present paper gives further development of the algebraic-combinatorial context for the description of the general classes of symmetric functions of π-type, introduced in our previous papers [8,9,10]. Specifically, further to the previously-derived π-type 'plethystic' vertex operators given as the algebraic tools for deriving the π-type symmetric functions as modal products, we have identified in this work the dual counterparts of these objects.…”
Section: Conclusion and Related Workmentioning
confidence: 85%
“…Our results from [7][8][9][10] are as follows. For each π we have identified in the ring of symmetric functions, the linear basis of symmetric functions of type π which plays the role of the universal character ring for the group H π , analogously to the way in which the standard basis of Schur functions, and Schur functions of symplectic and orthogonal type, provide the structure of the universal character rings in the general linear, orthogonal and symplectic cases (for the Hopf structure of the character rings in the latter cases see also [11]).…”
Section: Introductionmentioning
confidence: 87%
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