On association schemes with multiplicities 1 or 2

Mikhail Muzychuk, Bangteng Xu

Research output: Contribution to journalArticlepeer-review

Abstract

Inspired by the work of Amitsur [1] on finite groups whose irreducible characters all have degree (multiplicity) 1 or 2, in this paper we study association schemes whose irreducible characters all have multiplicity 1 or 2. We will first show that the general case can be reduced to commutative association schemes. Then for commutative association schemes with multiplicities 1 or 2, we prove that their Krein parameters are all rational integers. Using automorphism groups of association schemes, we obtain a characterization and classification of those commutative association schemes all valencies and multiplicities of which are 1 or 2 in terms of Cayley schemes.

Original languageEnglish
Pages (from-to)89-116
Number of pages28
JournalJournal of Algebra
Volume585
DOIs
StatePublished - 1 Nov 2021

Keywords

  • Association schemes
  • Automorphism groups
  • Cayley schemes
  • Krein parameters
  • Multiplicities
  • Quotient schemes

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