The center of the modular super Yangian $Y_{m|n}$

Abstract

The present paper is devoted to studying the super Yangian Y m|n associated to the general linear Lie superalgebra gl m|n over a field of positive characteristic. We extend Drinfeld-type presentations of Y m|n and the special super Yangian SY m|n to positive characteristic. Moreover, the center Z(Y m|n ) of Y m|n is described: it is generated by its Harish-Chandra center together with a large p-center. We also study the p-center of SY m|n and provide another description of the p-center of Y m|n in terms of the RTT generators. CONTENTS 1. Introduction 2. The current superalgebra 2.1. The current superalgebra 2.2. Symmetric invariants 2.3. Restricted Lie superalgebra 2.4. The center of U(g) 3. Modular super Yangian Y m|n and Drinfeld-type presentation 3.1. RTT presentation of Y m|n 3.2. Loop filtration 3.3. Gauss decomposition and quasideterminants 3.4. Maps between Super Yangians 3.5. Gauss decomposition of Y m|n 3.6. Drinfeld-type presentation 3.7. Automorphisms 4. The center of Y m|n 4.1. Harish-Chandra center 4.2. Off-diagonal p-central elements 4.3. Diagonal p-central elements 4.4. The center Z(Y m|n ) 5. Modular super Yangian of sl m|n 5.1. The special super Yangian 5.2. The p-centre of SY m|n 5.3. Another description of the p-center of Y m|n References