Generalised Verma modules for the orthosymplectic Lie superalgebra osp(k|2)

Abstract

The composition factors and their multiplicities are determined for generalised Verma modules over the orthosymplectic Lie superalgebra osp(k|2). The results enable us to obtain explicit formulae for the formal characters and dimensions of the finite-dimensional irreducible modules. Applying these results, we also compute the first and second cohomology groups of the Lie superalgebra with coefficients in finite-dimensional Kac modules and irreducible modules.

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References in corpus (3)

• Irreducible Characters of General Linear Superalgebra and Super Duality
• Highest weight categories arising from Khovanov's diagram algebra IV: the general linear supergroup
• Character Formulae for Ortho-symplectic Lie Superalgebras $\mathfrak{osp}(n|2)$

Cited by in corpus (4)

• Character and dimension formulae for queer Lie superalgebra
• Dualities for Lie superalgebras
• Generalized Verma Modules and Character Formulae for $\mathfrak{osp}(3|2m)$
• Generalised Jantzen filtration of Lie superalgebras I