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Convex bases of PBW type for quantum affine algebras

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Abstract

This note has two purposes. First we establish that the map defined in [L, Sect. 40.2.5 (a)] is an isomorphism for certain admissible sequences. Second we show the map gives rise to a convex basis of Poincaré-Birkhoff-Witt (PBW) type for U+, an affine untwisted quantized enveloping algebra of Drinfel's and Jimbo. The computations in this paper are made possible by extending the braid group action by certain outer automorphisms of the algebra.

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  1. Mathematics Department, M.I.T., 02139, Cambridge, MA, USA

    Jonathan Beck

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  1. Jonathan Beck
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Communicated by M. Jimbo

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Beck, J. Convex bases of PBW type for quantum affine algebras. Commun.Math. Phys. 165, 193–199 (1994). https://doi.org/10.1007/BF02099742

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  • DOI: https://doi.org/10.1007/BF02099742

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