zbMATH — the first resource for mathematics

Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras. (English) Zbl 0808.17005
The notion of a crystal base was introduced by Kashiwara and proved to exist uniquely for any integrable highest weight representation of the \(q\)-analogue of symmetrizable Kac-Moody Lie algebras. In the present paper the authors give their explicit description for finite dimensional irreducible representations of \(A_ n\), \(B_ n\), \(C_ n\) and \(D_ n\). In particular, in the \(A_ n\)-case the crystal bases are labelled by the semistandard tableaux. The description is concrete and self-contained.
Reviewer: H.Yamada (Tokyo)

17B37 Quantum groups (quantized enveloping algebras) and related deformations
Full Text: DOI