Monomial Realization of the Tensor Product of Crystals for Quantum Finite Algebras

Abstract

In this paper, we give a combinatorial description of the crystal bases of the tensor products of the irreducible highest weight modules over quantum finite algebras in terms of Nakajima monomials. Also, we explain how to decompose the tensor product of irreducible highest weight crystals into irreducibles by giving a bijection defined by multiplication of monomials.

Key Words:

• Crystals
• Nakajima monomials
• Tensor product decompositions

2010 AMS Subject Classification:

• 17B37
• 81R50

ACKNOWLEDGMENTS

The authors would like to express their sincere gratitude to the referee for careful reading and for valuable suggestions.

First author's work was supported by the 2011 Research Fund of the University of Seoul. Second author's research was supported by KOSEF Grant #2009-00688200.

Notes

Communicated by K. Misra.