Generic Extensions and Canonical Bases for Cyclic Quivers

Deng, Bangming ; Du, Jie ; Xiao, Jie

Canadian journal of mathematics, Tome 59 (2007) no. 6, pp. 1260-1283

Résumé

We use the monomial basis theory developed by Deng and Du to present an elementary algebraic construction of the canonical bases for both the Ringel–Hall algebra of a cyclic quiver and the positive part ${{\mathbf{U}}^{+}}$ of the quantum affine $\mathfrak{s}{{\mathfrak{l}}_{n}}$ . This construction relies on analysis of quiver representations and the introduction of a new integral PBW-like basis for the Lusztig $\mathbb{Z}[v,\,{{v}^{-1}}]$ -form of ${{\mathbf{U}}^{+}}$ .

Détail

DOI : 10.4153/CJM-2007-054-7

Mots-clés : 17B37, 16G20

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