Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras
Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras
Abstract We prove that the tensor product of a simple and a finite dimensional $${\mathfrak {sl}}_n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>sl</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math> -module has finite type socle. This is applied to reduce classification of simple $${\mathfrak {q}}(n)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>q</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> -supermodules to that of simple $${\mathfrak {sl}}_n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>sl</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math> -modules. Rough structure of simple $${\mathfrak …