Displaying similar documents to “The Robinson-Schensted correspondence, crystal bases, and the quantum straightening at q = 0 .”

Bar-invariant bases of the quantum cluster algebra of type A 2 ( 2 )

Xueqing Chen, Ming Ding, Jie Sheng (2011)

Czechoslovak Mathematical Journal

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We construct bar-invariant ℤ [ q ± 1 / 2 ] -bases of the quantum cluster algebra of the valued quiver A 2 ( 2 ) , one of which coincides with the quantum analogue of the basis of the corresponding cluster algebra discussed in P. Sherman, A. Zelevinsky: Positivity and canonical bases in rank 2 cluster algebras of finite and affine types, Moscow Math. J., 4, 2004, 947–974.

A U q ⁢ s ⁢ l ⁢ 2 -representation with no quantum symmetric algebra

Olivia Rossi-Doria (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We show by explicit calculations in the particular case of the 4-dimensional irreducible representation of U q ⁢ s ⁢ l ⁢ 2 that it is not always possible to generalize to the quantum case the notion of symmetric algebra of a Lie algebra representation.