The Terwilliger algebra of the incidence graphs of Johnson geometry

More on the Terwilliger algebra of Johnson schemes

In [F. Levstein, C. Maldonado, The Terwilliger algebra of the Johnson schemes, Discrete Math. 307 (2007) 1621--1635], the Terwilliger algebra of the Johnson scheme $J(n,d)$ was determined when $n\geq 3d$. In this paper, we determine the Terwilliger algebra ${\mathcal T}$ for the remaining case $2d\leq n<3d$.

Terwilliger algebra of Odd graphs

In [The Terwilliger algebra of the Johnson schemes, Discrete Mathematics 307 (2007) 1621--1635], Levstein and Maldonado computed the Terwilliger algebra of the Johnson scheme $J(n,m)$ when $3m\leq n$. The distance-$m$ graph of $J(2m+1,m)$ is the Odd graph $O_{m+1}$. In this paper, we determine the Terwilliger algebra of $O_{m+1}$ and give its basis.

Modular Terwilliger algebras of association schemes

We define modular Terwilliger algebras of association schemes, Terwilliger algebras over a positive characteristic field, and consider basic properties. We give a condition for the modular Terwilliger algebra to be non-semisimple. We show that the dimension of a Terwilliger algebra of a Johnson scheme depends on the characteristic of the coefficient field. We also give some other examples.

$U(\mathfrak{sl}_2)$ 的 Clebsch--Gordan 系数与 Johnson 图的 Terwilliger 代数

The Clebsch--Gordan coefficients of $U(\mathfrak{sl}_2)$ and the Terwilliger algebras of Johnson graphs

研究U(sl_2)的Clebsch-Gordan系数与Johnson图Terwilliger代数的联系，通过构造代数同态将张量积模分解为Hahn模，并用二项式系数表达Terwilliger代数维数。

$U_q(\mathfrak{sl}_2)$ 的 Clebsch–Gordan 系数与 Grassmann 图的 Terwilliger 代数之间一种不易察觉的联系

An imperceptible connection between the Clebsch--Gordan coefficients of $U_q(\mathfrak{sl}_2)$ and the Terwilliger algebras of Grassmann graphs

本文针对 q-模拟中原推导失效的问题，通过迂回构造建立 $U_q(\mathfrak{sl}_2)$ 的 Clebsch–Gordan 系数与 Grassmann 图 Terwilliger 代数之间的隐藏联系。

Codes and Designs in Johnson Graphs From Symplectic Actions on Quadratic Forms

The Johnson graph $J(v, k)$ has as vertices the $k$-subsets of $\mathcal{V}=\{1,\ldots, v\}$, and two vertices are joined by an edge if their intersection has size $k-1$. An \emph{$X$-strongly incidence-transitive code} in $J (v, k)$ is a proper vertex subset $Γ$ such that the subgroup $X$ of graph automorphisms leaving $Γ$ invariant is transitive on the set $Γ$ of `codewords', and for each codeword $Δ$, the setwise stabiliser $X_Δ$ is transitive on $Δ\times (\mathcal{V}\setminus Δ)$. We classify the \emph{$X$-strongly incidence-transitive codes} in $J(v,k)$ for which $X$ is the symplectic gro…