The perfect matching association scheme

Srinivasan, Murali K.¹

¹ Department of Mathematics Indian Institute of Technology Bombay Powai, Mumbai 400076, India

Algebraic Combinatorics, Tome 3 (2020) no. 3, pp. 559-591.

Résumé

We revisit the Bose–Mesner algebra of the perfect matching association scheme. Our main results are

• An inductive algorithm, based on solving linear equations, to compute the eigenvalues of the orbital basis elements given the central characters of the symmetric groups.
• Universal formulas, as content evaluations of symmetric functions, for the eigenvalues of fixed orbitals.
• An inductive construction of an eigenvector (the so called first Gelfand–Tsetlin vector) in each eigenspace leading to a different inductive algorithm (not using central characters) for the eigenvalues of the orbital basis elements.

Détail

Reçu le : 2018-08-13
Révisé le : 2019-11-28
Accepté le : 2019-11-29
Publié le : 2020-06-02
DOI : 10.5802/alco.104

Classification : 05E10, 05E05, 05E30
Mots-clés : perfect matching association scheme, content evaluation of symmetric functions, Gelfand–Tsetlin vectors.

Licence : CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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