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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.

Modular representations of the ortho‐symplectic supergroups