Abstract
We give an improved algorithm for the action of the divided power of a Chevalley basis element of an affine Lie algebra of type on canonical basis elements satisfying an easily checked uniformity condition and compare calculation times for our algorithm against the standard algorithm. For symmetric Kashiwara crystals of affine type and rank , 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 nonrecursive manner. In particular, for a symmetric crystal with , we give formulae for the canonical basis elements for all the -regular multipartitions with defects either or , for .
Citation
Ola Amara-Omari. Mary Schaps. "NONRECURSIVE CANONICAL BASIS COMPUTATIONS FOR LOW RANK KASHIWARA CRYSTALS OF TYPE ." Rocky Mountain J. Math. 52 (6) 1929 - 1955, December 2022. https://doi.org/10.1216/rmj.2022.52.1929
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