Tilting modules for classical Lie superalgebras

Chih Whi Chen, Shun Jen Cheng, Kevin Coulembier

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study tilting and projective-injective modules in a parabolic BGG category (Formula presented.) for an arbitrary classical Lie superalgebra. We establish a version of Ringel duality for this type of Lie superalgebras which allows to express the characters of tilting modules in terms of those of simple modules in that category. We also obtain a classification of projective-injective modules in the full BGG category (Formula presented.) for all simple classical Lie superalgebras. We then classify and give an explicit combinatorial description of parabolic subalgebras of the periplectic Lie superalgebras and apply our results to study their tilting modules in more detail.

Original languageEnglish
Pages (from-to)870-900
Number of pages31
JournalJournal of the London Mathematical Society
Volume103
Issue number3
DOIs
StatePublished - Apr 2021

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