Nonrecursive canonical basis computations for low rank Kashiwara crystals of type A

Ola Amara-Omari; Mary Schaps

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arXiv · 2007.14650

Nonrecursive canonical basis computations for low rank Kashiwara crystals of type A

Ola Amara-Omari·Mary Schaps

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Abstract

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 $0 \leq k \leq a$.

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BibTeX RIS

Ola Amara-Omari, Mary Schaps. 2020-07-29. Nonrecursive canonical basis computations for low rank Kashiwara crystals of type A. https://arxiv.org/abs/2007.14650

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