Integral forms for Yangians of classical type

Abstract

Let $\mathfrak{g}$ be a simple Lie algebra of classical type. We construct a $\mathbb{Z}[1/2]$-integral form of the Yangian $Y(\mathfrak{g})$ generated by divided powers of the positive and negative Drinfeld generators, and establish its triangular decomposition and PBW basis. Under the loop filtration, its associated graded algebra is the current algebra part of Garland's integral form. As applications, over an algebraically closed field of characteristic $p>3$, we identify the small Yangian with the restricted Yangian and classify their finite dimensional simple modules in terms of restricted Drinfeld polynomials.

arXiv commentv1 28 pages, comments welcome!; v2 43 pages, classified finite dimensional simple modules of small and restricted Yangians by restricted Drinfeld polynomials; revised the introduction and exposition