Abstract
Let be a hyperbolic Kac-Moody algebra of rank 2. We give a necessary and sufficient condition for the crystal graph of the Lakshmibai-Seshadri path crystal to be connected for an arbitrary integral weight λ.
Acknowledgments
The author would like to thank Daisuke Sagaki, who is his supervisor, for his kind support and advice. Also, he is grateful to the referee for valuable comments and suggestions.