Character tables of certain association schemes coming from finite unitary and symplectic groups
TLDR
In this article, the character tables of the association schemes obtained from the action of finite unitary groups acting on the set of nonisotropic projective points and finite group PGL(2, q) on the cosets by cyclic subgroups Zq + 1 and Zq − 1 were studied.About:
This article is published in Journal of Algebra.The article was published on 1991-12-01 and is currently open access. It has received 11 citations till now. The article focuses on the topics: Character table & Association scheme.read more
Citations
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Finite analogues of non-Euclidean spaces and Ramanujan graphs
TL;DR: This paper obtains further examples of families of Ramanujan graphs, by using previous works on association schemes and the calculations of their character tables, which are in some sense analogues of the finite upper half planes over finite fields, i.e., finite versions of non-Euclidean spaces.
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Character Tables of Fission Schemes and Fusion Schemes
Euchi Bannai,Sung Y. Song +1 more
TL;DR: It is shown that if each class Sj of Y is either equal to Ri for some i or obtained by fusing two Ri's in a simple uniform pattern, then the character table of one is determined by the other, and this fact is proved by orthogonality relation of the character tables.
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Explicit Ramsey graphs and Erdos distance problem over finite Euclidean and non-Euclidean spaces
TL;DR: In this article, the Erdos distance problem over finite Euclidean and non-Euclidean spaces is studied, and the main tools are graphs associated to finite-dimensional spaces that are considered in Bannai-Shimabukuro-Tanaka (2004, 2007).
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Finite Euclidean graphs and Ramanujan graphs
TL;DR: Finite analogues of Euclidean graphs in a more general setting are considered and the ideas of controlling association schemes, and the Ennola type dualities, are used in the previous work on the character tables of commutative association schemes.
References
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Tables of the association schemes of finite orthogonal groups acting on the nonisotropic points
TL;DR: The character tables of the association schemes obtained from the actions of finite (simple) orthogonal groups are studied to show that they are controlled by the character table of the group PSL (2, q).
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The Character Tables of Paige's Sample Moufang Loops and Their Relationship to the Character Tables of Psl(2, q)
Eiichi Bannai,Sung-Yell Song +1 more
Using finite unitary geometry to construct a class of pbib designs
TL;DR: In this article, the authors considered the n-dimensional (n≥3)unitary geometry over finite field F(q~2), where q is a power of a prime, and obtained an association scheme and PBIB designs with q associate classes.