Abstract
In this paper, we give an insertion scheme for the tableaux of Kashiwara– Nakashima realizing the crystal bases of the irreducible highest weight modules over the classical Lie algebras. It gives an explicit combinatorial description of the decomposition of the tensor product V(λ) ⊗ V(μ) into irreducible modules.
Mathematics Subject Classification:
Acknowledgments
This research was supported by KOSEF Grant # 98-0701-01-5-L and BK21 Mathematical Sciences Division, Seoul National University.
Part of this work was completed while the authors were visiting the Department of Mathematics of University of Wisconsin, Madison. We would like to express our sincere gratitude to the Department of Mathematics of University of Wisconsin, Madison for their hospitality and support during our visit. Special thanks should be given to Professor Georgia Benkart, Professor Chanyoung Lee Shader and Professor Itaru Terada for their interest in this work and many valuable discussions. We would also like to express our sincere gratitude to Professor S.-J. Kang for his guidance, encouragement, and many valuable suggestions.
Note. After we wrote this paper, we were informed that T. Baker and C. Lecouvey have obtained essentially the same insertion scheme independently by different approach (Baker, Citation2000a Citation2000b; Lecouvey, Citation2002).
Notes
#Communicated by K. Misra.