Nonrecursive canonical basis computations for low rank Kashiwara crystals of type A
| Autor: | Amara-Omari, Ola, Schaps, Mary |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | For symmetric Kashiwara crystals of type $A$ and rank $e=2$, and for the canonical basis elements that we call external, corresponding to weights on the outer skin of the Kashiwara crystal, we construct the canonical basis elements in a non-recursive manner. In particular, for a symmetric crystal with $\Lambda=a \Lambda_0+a \Lambda_1$, we give formulae for the canonical basis elements for all the $e$-regular multipartitions with defects either $k(a-k)$ or $k(a-k)+2a$, for $0 \leq k \leq a$. Comment: 21 pages, 1 figure; typos corrected |
| Databáze: | arXiv |
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