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July 2010 A new description of convex bases of PBW type for untwisted quantum affine algebras
Ken Ito
Hiroshima Math. J. 40(2): 133-183 (July 2010). DOI: 10.32917/hmj/1280754419

Abstract

In [8] we classified all ``convex orders'' on the positive root system $\Delta_+$ of an arbitrary untwisted affine Lie algebra ${\mathfrak g}$ and gave a concrete method of constructing all convex orders on $\Delta_+$. The aim of this paper is to give a new description of ``convex bases'' of PBW type of the positive subalgebra $U^+$ of the quantum affine algebra $U=U_q({\mathfrak g})$ by using the concrete method of constructing all convex orders on $\Delta_+$. Applying convexity properties of the convex bases of $U^+$, for each convex order on $\Delta_+$, we construct a pair of dual bases of $U^+$ and the negative subalgebra $U^-$ with respect to a $q$-analogue of the Killing form, and then present the multiplicative formula for the universal $R$-matrix of $U$.

Citation

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Ken Ito. "A new description of convex bases of PBW type for untwisted quantum affine algebras." Hiroshima Math. J. 40 (2) 133 - 183, July 2010. https://doi.org/10.32917/hmj/1280754419

Information

Published: July 2010
First available in Project Euclid: 2 August 2010

zbMATH: 1217.17008
MathSciNet: MR2680654
Digital Object Identifier: 10.32917/hmj/1280754419

Subjects:
Primary: 17B37
Secondary: 17B67, 20F55

Rights: Copyright © 2010 Hiroshima University, Mathematics Program

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Vol.40 • No. 2 • July 2010
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