Geodesic
The subconstituent algebra of an association scheme. I
Journal of Algebraic Combinatorics, Tome 1 (1992) no. 4, pp. 363-388.

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Summary: We introduce a method for studying commutative association schemes with $\mathbb C$ mathbbC -algebra $T = T( x)$ whose structure reflects the combinatorial structure of $Y$. We call T the subconstituent algebra of Y with respect to x. Roughly speaking, $T$ is a combinatorial analog of the centralizer algebra of the stabilizer of $x$ in the automorphism group of $Y$. In general, the structure of $T$ is not determined by the intersection numbers of $Y$, but these parameters do give some information. Indeed, we find a relation among the generators of $T$ for each vanishing intersection number or Krein parameter.
Keywords: association scheme, $P$-polynomial, $Q$-polynomial, distance-regular graph 
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     author = {Terwilliger, Paul},
     title = {The subconstituent algebra of an association scheme. {I}},
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Terwilliger, Paul. The subconstituent algebra of an association scheme. I. Journal of Algebraic Combinatorics, Tome 1 (1992) no. 4, pp. 363-388. http://geodesic.mathdoc.fr/item/JAC_1992__1_4_a0/