Abstract
In this paper, we study the representations of the periplectic Lie superalgebra using the Duflo–Serganova functor. Given a simple p(n)module L and a certain odd element x ∈ p(n) of rank 1, we give an explicit description of the composition factors of the p(n−1)module DS_{x} (L), which is defined as the homology of the complex ∏M^{x}−→ M^{x}−→ ∏M, where ∏ denotes the paritychange functor (−) ⊗ ℂ^{01}. In particular, we show that this p(n−1)module is multiplicityfree. We then use this result to give a simple explicit combinatorial formula for the superdimension of a simple integrable finitedimensional p(n)module, based on its highest weight. In particular, this reproves the Kac–Wakimoto conjecture for p(n), which was proved earlier by the authors.
Original language  English 

Pages (fromto)  697729 
Number of pages  33 
Journal  Algebra and Number Theory 
Volume  16 
Issue number  3 
DOIs 

State  Published  1 Jan 2022 
Keywords
 Duflo–Serganova functor
 Lie superalgebra
 periplectic Lie superalgebra
 superdimension
ASJC Scopus subject areas
 Algebra and Number Theory