The number of multiplicity-free primitive ideals associated with the rigid nilpotent orbits

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Abstract

In this paper we describe the number of multiplicity-free primitive ideals associated with the rigid nilpotent orbits in finite-dimensional simple Lie algebras. Thanks to the results obtained earlier we need to solve the problem for the two largest rigid nilpotent orbits in Lie algebras of type ${\rm E}_8$. As a corollary we compute the number of small modules in the corresponding reduced enveloping algebras over algebraically closed fields of characteristic $p>5$.
Original languageEnglish
PublisherInternational Press
Publication statusAccepted/In press - 26 Nov 2022

Publication series

NamePure and Applied Mathematics Quarterly
PublisherInternational Press

Keywords

  • math.RT
  • 17B35, 17B50 (Primary) 17B20 (Secondary)

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