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| Hypercube and Tetrahedron Algebra |
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Citation： |
Bo HOU,Suogang GAO.Hypercube and Tetrahedron Algebra[J].Chinese Annals of Mathematics B,2015,36(2):293~306 |
| Page view： 2497
Net amount： 1860 |
Authors： |
Bo HOU; Suogang GAO; |
Foundation： |
the National Natural Science Foundation of China (Nos. 11471097,
11271257), the Specialized Research Fund for the Doctoral Program of Higher Education of China
(No. 20121303110005), the Natural Science Foundation of Hebei Province (No.A2013205021) and the
Key Fund Project of Hebei Normal University (No. L2012Z01). |
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| Abstract： |
Let $D$ be an integer at least $3$ and let $H(D,2)$ denote the
hypercube. It is known that $H(D,2)$ is a $Q$-polynomial
distance-regular graph with diameter $D$, and its eigenvalue
sequence and its dual eigenvalue sequence are all
$\{D-2i\}_{i=0}^D$. Suppose that $\boxtimes$ denotes the tetrahedron
algebra. In this paper, the authors display an action of $\boxtimes$
on the standard module $V$ of $H(D,2)$. To describe this action, the
authors define six matrices in ${\rm{Mat}}_X(\mathbb{C})$, called
\begin{align*}
\label{eq11}A,\ A^*,\ B,\ B^*,\ K,\ K^*.
\end{align*}
Moreover, for each matrix above, the authors compute the transpose
and then compute the transpose of each generator of $\boxtimes$ on
$V$. |
Keywords： |
Tetrahedron algebra, Hypercube, Distance-regular graph, Onsager algebra |
Classification： |
05E30, 05C50, 17B65 |
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