Affine periplectic Brauer algebras

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Abstract

We formulate Nazarov–Wenzl type algebras Pˆd for the representation theory of the periplectic Lie superalgebras p(n). We establish an Arakawa–Suzuki type functor to provide a connection between p(n)-representations and Pˆd -representations. We also consider various tensor product representations for Pˆd . The periplectic Brauer algebra Ad developed by Moon is a quotient of Pˆd . In particular, actions induced by Jucys–Murphy elements can also be recovered under the tensor product representation of Pˆd . Moreover, a Poincare–Birkhoff–Witt type basis for Pˆd is obtained. A diagram realization of Pˆd is also obtained.

Original languageEnglish
Pages (from-to)345-372
Number of pages28
JournalJournal of Algebra
Volume501
DOIs
StatePublished - 1 May 2018

Keywords

  • Affine Nazarov–Wenzl algebra
  • Jucys–Murphy elements
  • Marked Brauer category
  • Periplectic Brauer algebra
  • Periplectic Lie superalgebras
  • Poincare–Birkhoff–Witt basis

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