Clifford type theorems for association schemes and their algebraic fusions

We investigate the relationship between complex characters of association schemes and their fusion schemes. We first prove Frobenius reciprocity between the irreducible representations of finite schemes and their fusion schemes, and add a formula on multiplicities. After that, we provide Clifford type theorems for association schemes and their algebraic fusions.ArticleJOURNAL OF ALGEBRA. 363:1-7 (2012)journal articl

Radicals of SnS_n-invariant positive semidefinite hermitian forms

Let G be a finite group, V a complex permutation module for G over a finite G-set X, and f:V 7V\u2192C a G-invariant positive semidefinite hermitian form on V. In this paper we show how to compute the radical V a5 of f, by extending to nontransitive actions the classical combinatorial methods from the theory of association schemes. We apply this machinery to obtain a result for standard Majorana representations of the symmetric groups

On algebraic fusions of association schemes

We give a complete description of the irreducible representations of algebraic fusions of association schemes, in terms of the irreducible representations of a Schur cover of the corresponding group of algebraic automorphisms.Comment: This paper has been withdrawn by one of the authors, since it requires more wor

The Ring of Support-Classes of SL_2(F_q)\mathrm{SL}\_2(\mathbb F\_q)

We introduce and study a subring $\mathcal{SC}$ of $\mathbb Z[\mathrm{SL}\_2(\mathbb F\_q)]$ obtained by summing elements of $\mathrm{SL}\_2(\mathbb F\_q)$ according to their support. The ring $\mathcal SC$ can be used for the construction of several association schemes