Modular representations of the ortho-symplectic supergroups

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 ingredient 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.

v2, 23 pages, updated references and minor changes, to appear in Proc. London Math. Soc

References in corpus (1)

• A new proof of the Mullineux conjecture

Cited by in corpus (22)

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• Borel-Weil Theorem for Algebraic Supergroups
• Finite $W$-superalgebras and the dimensional lower bounds for the representations of basic Lie superalgebras
• Dualities for Lie superalgebras
• Chevalley Supergroups of type D(2,1;a)
• Polynomial super representations of the hyperalgebra of ${\mathfrak{gl}}_{m|n}$ at roots of unity
• Finite W-superalgebras for basic Lie superalgebras
• Classification of irreducible representations of affine group superschemes and the division superalgebras of their endomorphisms
• Frobenius kernels of algebraic supergroups and Steinberg's tensor product theorem
• Finite W-superalgebras for basic classical Lie superalgebras
• Algebraic supergroups and Harish-Chandra pairs over a commutative ring
• Support varieties and representations of tame basic classical Lie superalgebras
• $GL(m|n)$-supermodules with good and Weyl filtrations
• The Steinberg Tensor Product Theorem for General Linear Group Schemes in the Verlinde Category
• Representation Theory of Symmetric Groups and Related Hecke Algebras
• Modular representations of exceptional supergroups
• Super Vust theorem and Schur-Sergeev duality for principal finite $W$-superalgebras
• Jantzen filtration and strong linkage principle for modular Lie superalgebras