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

Fabio Gavarini
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Abstract

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

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Fabio Gavarini. 2017-05-15. A PBW basis for Lusztig's form of untwisted affine quantum groups. https://doi.org/10.1080/00927879908826468

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