# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# Dual polar graphs and the quantum algebra $U_q(sl_2)$

Presented by Mr. Chalermpong WORAWANNOTAI
Type: Oral presentation
Track: Representations of Graphs

## Content

Let $\Gamma = (X,R)$ denote a dual polar graph. Let $A$ denote the adjacency matrix of $\Gamma$. Fix a vertex $x \in X$. Let $A^* = A^*(x)$ denote the dual adjacency matrix of $\Gamma$ with respect to $x$. Let $T = T(x)$ denote the subalgebra of $\mbox{Mat}_X(\C)$ generated by $A,A^*$. Let $V = \C^X$; view $V$ as a left $T$-module. In this talk we discuss certain nice maps in $T$ and show how they naturally give a $U_q(\mathfrak{sl}_2)$-module structure on $V$.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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