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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


We study the Yangian Yn associated to the general linear Lie algebra 𝔤𝔩n over a field of positive characteristic, as well as its shifted analog Yn(σ). Our main result gives a description of the centre of Yn(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, Yn(σ) is free as a module over its center. In future work, it will be seen that every reduced enveloping algebra Uχ(𝔤𝔩n) 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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