Moscow Mathematical Journal

Volume 18, Issue 4, October–December 2018 pp. 617–657.

The p-Centre of Yangians and Shifted Yangians

Authors: Jonathan Brundan (1) and Lewis Topley (2)
Author institution:(1) Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
(2) School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7FS United Kingdom

Summary:

We study the Yangian Y_n associated to the general linear Lie algebra 𝔤𝔩_n over a field of positive characteristic, as well as its shifted analog Y_n(σ). Our main result gives a description of the centre of Y_n(σ): it is a polynomial algebra generated by its Harish-Chandra centre (which lifts the centre in characteristic zero) together with a large p-centre. Moreover, Y_n(σ) is free as a module over its center. In future work, it will be seen that every reduced enveloping algebra U_χ(𝔤𝔩_n) is Morita equivalent to a quotient of an appropriate choice of shifted Yangian, and so our results will have applications in classical representation theory.

2010 Math. Subj. Class. Primary: 17B37.

Keywords: Modular Yangian, finite W-algebra, restricted Lie algebra, centre.

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