Crystal Bases and Young Tableaux

Details Crystal Bases and Young Tableaux Crystal Bases and Young Tableaux

1997-06-19

arxiv.org/abs/q-alg/9706025v1

Mathematics

Quantum Algebra

23 pages, plain TeX

Scientific paper

Let B be the crystal basis of the minus part of the quantized enveloping algebra of a semi-simple Lie algebra. Kashiwara has shown that B has a combinatorial description in terms of an embedding of B into the tensor product of B and k abstract crystals B_{i_j}, j=1,2,...,k, where the longest word in the Weyl group is s_{i_1}...s_{i_k}. We give an explicit description of the image of this embedding for classical Lie algebras of types A, B, C, D. This description is in terms of semi-standard Young tableaux of types A, B, C, D defined by Kashiwara and Nakashima.

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