dorsal/arxiv
View SchemaCrystal Bases and Young Tableaux
| Authors | Gerald Cliff |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9706025 |
| URL | https://arxiv.org/abs/q-alg/9706025 |
Abstract
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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"abstract": "Let B be the crystal basis of the minus part of the quantized enveloping\nalgebra of a semi-simple Lie algebra. Kashiwara has shown that B has a\ncombinatorial description in terms of an embedding of B into the tensor product\nof B and k abstract crystals B_{i_j}, j=1,2,...,k, where the longest word in\nthe Weyl group is s_{i_1}...s_{i_k}. We give an explicit description of the\nimage of this embedding for classical Lie algebras of types A, B, C, D. This\ndescription is in terms of semi-standard Young tableaux of types A, B, C, D\ndefined by Kashiwara and Nakashima.",
"arxiv_id": "q-alg/9706025",
"authors": [
"Gerald Cliff"
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"q-alg",
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"title": "Crystal Bases and Young Tableaux",
"url": "https://arxiv.org/abs/q-alg/9706025"
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