Talk:Crystal base
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[edit]This article confuses crystal bases and canonical bases. The definition in the main body of the article is that of crystal bases which are bases of certain algebras or representations at q=0. Canonical bases are bases of the same objects at any q which can in particular be specialized at q=0 when they become crystal bases. The references are also not correct. The paper Kashiwara (1990) constructs the crystal bases for representations in classical types and conjectures that this can be extended to exceptional types. The paper Lusztig (1990) contains the first construction of the canonical bases (including in exceptional types) and in particular the crystal bases (including in exceptional types). A second construction of canonical and in particular crystal bases (for general types) was then given in Kashiwara (1991). 173.76.154.248 (talk) 15:26, 21 January 2015 (UTC) 173.76.154.248 (talk) 03:23, 25 January 2015 (UTC)