An inequality in character algebras

In this paper, we prove the following: Theorem. Let A=〈A0,A1,..,A(d) 〉 denote a complex character algebra with d2 which is P-polynomial with respect to the ordering A 0,A 1,..,A d of the distinguished basis. Assume that the structure constants p ijh are all nonnegative and the Krein parameters q ijh...

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Main Author: Pascasio, Arlene A.
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Published: Animo Repository 2003
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Online Access:https://animorepository.dlsu.edu.ph/faculty_research/1995
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spelling oai:animorepository.dlsu.edu.ph:faculty_research-29942021-08-07T07:55:38Z An inequality in character algebras Pascasio, Arlene A. In this paper, we prove the following: Theorem. Let A=〈A0,A1,..,A(d) 〉 denote a complex character algebra with d2 which is P-polynomial with respect to the ordering A 0,A 1,..,A d of the distinguished basis. Assume that the structure constants p ijh are all nonnegative and the Krein parameters q ijh are all nonnegative. Let θ and θ′ denote eigenvalues of A 1, other than the valency k=k 1. Then the structure constants a 1=p 111 and b 1=p 121 satisfyθ+ k a1+1θ′+ k a1+1-ka1b1 (a1+1) 2.Let E and F denote the primitive idempotents of A associated with θ and θ′, respectively. Equality holds in the above inequality if and only if the Schur product E°F is a scalar multiple of a primitive idempotent of A. The above theorem extends some results of Jurišić, Koolen, Terwilliger, and the present author. These people previously showed the above theorem holds for those character algebras isomorphic to the Bose-Mesner algebra of a distance-regular graph. © 2002 Elsevier Science B.V. All rights reserved. 2003-03-06T08:00:00Z text https://animorepository.dlsu.edu.ph/faculty_research/1995 Faculty Research Work Animo Repository Association schemes (Combinatorial analysis) Representations of Lie algebras Mathematics
institution De La Salle University
building De La Salle University Library
continent Asia
country Philippines
Philippines
content_provider De La Salle University Library
collection DLSU Institutional Repository
topic Association schemes (Combinatorial analysis)
Representations of Lie algebras
Mathematics
spellingShingle Association schemes (Combinatorial analysis)
Representations of Lie algebras
Mathematics
Pascasio, Arlene A.
An inequality in character algebras
description In this paper, we prove the following: Theorem. Let A=〈A0,A1,..,A(d) 〉 denote a complex character algebra with d2 which is P-polynomial with respect to the ordering A 0,A 1,..,A d of the distinguished basis. Assume that the structure constants p ijh are all nonnegative and the Krein parameters q ijh are all nonnegative. Let θ and θ′ denote eigenvalues of A 1, other than the valency k=k 1. Then the structure constants a 1=p 111 and b 1=p 121 satisfyθ+ k a1+1θ′+ k a1+1-ka1b1 (a1+1) 2.Let E and F denote the primitive idempotents of A associated with θ and θ′, respectively. Equality holds in the above inequality if and only if the Schur product E°F is a scalar multiple of a primitive idempotent of A. The above theorem extends some results of Jurišić, Koolen, Terwilliger, and the present author. These people previously showed the above theorem holds for those character algebras isomorphic to the Bose-Mesner algebra of a distance-regular graph. © 2002 Elsevier Science B.V. All rights reserved.
format text
author Pascasio, Arlene A.
author_facet Pascasio, Arlene A.
author_sort Pascasio, Arlene A.
title An inequality in character algebras
title_short An inequality in character algebras
title_full An inequality in character algebras
title_fullStr An inequality in character algebras
title_full_unstemmed An inequality in character algebras
title_sort inequality in character algebras
publisher Animo Repository
publishDate 2003
url https://animorepository.dlsu.edu.ph/faculty_research/1995
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