A PBW basis for Lusztig's form of untwisted affine quantum groups

Details A PBW basis for Lusztig's form of untwisted affine quantum groups A PBW basis for Lusztig's form of untwisted affine quantum groups

1997-06-17

arxiv.org/abs/q-alg/9706018v4

Mathematics

Quantum Algebra

17 pages, AMS-TeX C, Version 2.1c. To appear in "Communications in Algebra"). In this version the last section has been shorte

Scientific paper

Let g be an untwisted affine Kac-Moody algebra over the field K, and let U_q(g) be the associated quantum enveloping algebra; let \hat{U}_q(g) be the Lusztig's integer form of U_q(g), generated by q-divided powers of Chevalley generators over a suitable subring R of K(q). We prove a Poincare`-Birkhoff-Witt like theorem for \hat{U}_q(g), yielding a basis over R made of ordered products of q-divided powers of suitable quantum root vectors.

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