In this note we determine when an induced supermodule HG 0(λ), corresponding to a dominant integral highest weight λ of the general linear supergroup G=GL(m|n), is irreducible. Using the contravariant duality given by the supertrace we obtain a characterization of irreducibility of Weyl supermodules V(λ). This extends the result of Kac (, ) who proved that, for ground fields of characteristic zero, V(λ) is irreducible if and only if λ is typical.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory