The Primitive Spectrum and Category O for the Periplectic Lie Superalgebra

Chih Whi Chen, Kevin Coulembier

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3 Scopus citations

Abstract

We solve two problems in representation theory for the periplectic Lie superalgebra , namely, the description of the primitive spectrum in terms of functorial realisations of the braid group and the decomposition of categoryinto indecomposable blocks. To solve the first problem, we establish a new type of equivalence between categoryfor all (not just simple or basic) classical Lie superalgebras and a category of Harish-Chandra bimodules. The latter bimodules have a left action of the Lie superalgebra but a right action of the underlying Lie algebra. To solve the second problem, we establish a BGG reciprocity result for the periplectic Lie superalgebra.

Original languageEnglish
Pages (from-to)625-655
Number of pages31
JournalCanadian Journal of Mathematics
Volume72
Issue number3
DOIs
StatePublished - 1 Jun 2020

Keywords

  • block decomposition
  • category O
  • completion functors
  • Harish-Chandra bimodules
  • periplectic Lie superalgebra
  • primitive spectrum
  • twisting functors

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