Zigzag Strip Bundles and the Crystal B(∞) for Quantum Affine Algebras

Abstract

We give a new realization of the crystal B(∞) of (, , or ) using the combinatorial objects zigzag strip bundles. Moreover, we study the relation between zigzag strip bundle realization, Nakajima monomial realization, and polyhedral realization of B(∞).

Key Words:

• Crystals
• Zigzag strip bundles

2010 Mathematics Subject Classification:

• 17B37
• 81R50

ACKNOWLEDGMENT

Part of this work was done during the authors visited KIAS, in the fall of 2009. They would like to express their sincere gratitude to the staff of KIAS for their hospitality and support. They also would like to thank Daehong Kim for pointing out inaccuracies in the previous version of this paper.

Notes

Communicated by K. Misra.