Crystal B(lambda) as a Subset of the Tableau Description of B(infinity) for the Classical Lie Algebra Types

Abstract

The irreducible highest weight crystal is known to appear as a connected component within the crystal graph of . Using the marginally large tableau realization of , we identify the elements belonging to this connected component, for the Lie algebra types C (n) , B (n) , and D (n+1). This gives us a tableau realization of that is different from the well known tableau realization by Kashiwara and Nakashima. In particular, our new description no longer involves half-boxes. We further present a description of through the Kashiwara embedding.