Modular representations of the ortho-symplectic supergroups

2007/06/30 by Bin Shu, Weiqiang Wang · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Affine Lie algebra #Algebra over a field #Algebraic structures and combinatorial models #Algebraically closed field #Combinatorics #Lie superalgebra #Mathematics #Moment map #Prime (order theory) #Pure mathematics #Supergroup #Symplectic geometry #Symplectic group #Symplectic representation #Tensor product #math.QA #math.RT

paper · pdf · doi:10.1112/plms/pdm040

published as Proc. London Math. Soc. 96 (2008), 251--271. · v2, 23 pages, updated references and minor changes, to appear in Proc. London Math. Soc

arxiv created 2007/09/02 · openalex publication_date 2007/10/17 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A Chevalley type integral basis for the ortho-symplectic Lie superalgebra is constructed. The simple modules of the ortho-symplectic supergroup over an algebraically closed field of prime characteristic not equal to 2 are classified, where a key combinatorial component comes from the Mullineux conjecture on modular representations of the symmetric group. A Steinberg tensor product theorem for the ortho-symplectic supergroup is also obtained.

Cited by

• GL(m|n)-supermodules with good and Weyl filtrations
• Borel-Weil theorem for algebraic supergroups

Related

• Linkage principle for ortho-symplectic supergroups
• The first fundamental theorem of invariant theory for the orthosymplectic supergroup
• A general approach to constructing minimal representations of Lie supergroups
• Central extensions of generalized orthosymplectic Lie superalgebras
• The second fundamental theorem of invariant theory for the orthosymplectic supergroup