Geodesic
Terwilliger algebras of wreath products of one-class association schemes
Journal of Algebraic Combinatorics, Tome 31 (2010) no. 3, pp. 455-466.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we study the wreath product of one-class association schemes $K _{ n }= H(1, n)$ for $n\geq 2$. We show that the $d$-class association scheme $K _{ n $_1$\wr K _{ n $_2$\wr $frac14 $\wr K _{ n $_ d K_n_1$\wr $K_n_2$\wr \cdots \wr $K_n_d formed by taking the wreath product of $K _{ n $_ i K_n_i (for $n _{ i }\geq 2$) has the triple-regularity property. Then based on this fact, we determine the structure of the Terwilliger algebra of $K _{ n $_1$\wr K _{ n $_2$\wr $frac14 $\wr K _{ n $_ d K_n_1$\wr $K_n_2$\wr \cdots \wr $K_n_d by studying its irreducible modules. In particular, we show that every non-primary module of this algebra is 1-dimensional.
Keywords: keywords commutative association schemes, Terwilliger algebra, wreath product 
@article{JAC_2010__31_3_a0,
     author = {Bhattacharyya, Gargi and Song, Sung Y. and Tanaka, Rie},
     title = {Terwilliger algebras of wreath products of one-class association schemes},
     journal = {Journal of Algebraic Combinatorics},
     pages = {455--466},
     publisher = {mathdoc},
     volume = {31},
     number = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2010__31_3_a0/}
}
TY  - JOUR
AU  - Bhattacharyya, Gargi
AU  - Song, Sung Y.
AU  - Tanaka, Rie
TI  - Terwilliger algebras of wreath products of one-class association schemes
JO  - Journal of Algebraic Combinatorics
PY  - 2010
SP  - 455
EP  - 466
VL  - 31
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2010__31_3_a0/
LA  - en
ID  - JAC_2010__31_3_a0
ER  - 
%0 Journal Article
%A Bhattacharyya, Gargi
%A Song, Sung Y.
%A Tanaka, Rie
%T Terwilliger algebras of wreath products of one-class association schemes
%J Journal of Algebraic Combinatorics
%D 2010
%P 455-466
%V 31
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2010__31_3_a0/
%G en
%F JAC_2010__31_3_a0
Bhattacharyya, Gargi; Song, Sung Y.; Tanaka, Rie. Terwilliger algebras of wreath products of one-class association schemes. Journal of Algebraic Combinatorics, Tome 31 (2010) no. 3, pp. 455-466. http://geodesic.mathdoc.fr/item/JAC_2010__31_3_a0/