Vol. 16, No. 3, 2022

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 10, 1681–1865
Issue 9, 1533–1680
Issue 8, 1359–1532
Issue 7, 1239–1357
Issue 6, 1127–1237
Issue 5, 981–1126
Issue 4, 805–980
Issue 3, 541–804
Issue 2, 267–539
Issue 1, 1–266

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Duflo–Serganova functor and superdimension formula for the periplectic Lie superalgebra

Inna Entova-Aizenbud and Vera Serganova

Vol. 16 (2022), No. 3, 697–729
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(n1)-module DS x(L), which is defined as the homology of the complex

ΠM xM xΠM,

where Π denotes the parity-change functor () 0|1.

In particular, we show that this 𝔭(n1)-module is multiplicity-free.

We then use this result to give a simple explicit combinatorial formula for the superdimension of a simple integrable finite-dimensional 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.

To Pavel Etingof for his 50th birthday.

Keywords
Lie superalgebra, periplectic Lie superalgebra, superdimension, Duflo–Serganova functor
Mathematical Subject Classification
Primary: 17B10, 17B55
Milestones
Received: 13 April 2020
Revised: 13 June 2021
Accepted: 24 July 2021
Published: 9 July 2022
Authors
Inna Entova-Aizenbud
Department of Mathematics
Ben-Gurion University
Beer-Sheva
Israel
Vera Serganova
Department of Mathematics
University of California at Berkeley
Berkeley, CA
United States