2019/03/07 by Simon M. Goodwin, Goodwin, Simon M., Lewis Topley +1 · 1 citation
Mathematics · #17B10 #17B37 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.QA #math.RA #math.RT #msc:17B10 #msc:17B37
paper · pdf · doi:10.48550/arxiv.1903.03079
38 pages. Comments welcome
arxiv created 2019/03/07 · openalex publication_date 2019/03/07 · arxiv updated 2019/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the truncated shifted Yangian Yn,l(σ) over an algebraically closed field \mathbbk of characteristic p > 0, which is known to be isomorphic to the finite W-algebra U(\mathfrakg, e) associated to a corresponding nilpotent element e∈ \mathfrakg = \mathfrakglN(\mathbbk). We obtain an explicit description of the centre of Yn,l(σ), showing that it is generated by its Harish-Chandra centre and its p-centre. We define Yn,l[p](σ) to be the quotient of Yn,l(σ) by the ideal generated by the kernel of trivial character of its p-centre. Our main theorem states that Yn,l[p](σ) is isomorphic to the restricted finite W-algebra U[p](\mathfrakg,e). As a consequence we obtain an explicit presentation of this restricted W-algebra.