Equivalence of blocks for the general linear Lie superalgebra

Abstract

We develop a reduction procedure which provides an equivalence (as highest weight categories) from an arbitrary block (defined in terms of the central character and the integral Weyl group) of the BGG category O for a general linear Lie superalgebra to an integral block of O for (possibly a direct sum of) general linear Lie superalgebras. We also establish indecomposability of blocks of O.

Formulation of Theorem 2.1 fixed in the last version

References in corpus (1)

• Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra q(n)

Cited by in corpus (22)

• Tensor product categorifications and the super Kazhdan-Lusztig conjecture
• Whittaker modules for classical Lie superalgebras
• The primitive spectrum of basic classical Lie superalgebras
• Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras
• \vS{a}povalov elements and the Jantzen sum formula for contragredient Lie superalgebras
• The primitive spectrum for gl(m|n)
• Reduction method for representations of queer Lie superalgebras
• Homological invariants in category O for the general linear superalgebra
• Some homological properties of category O. III
• Gorenstein homological algebra for rngs and Lie superalgebras
• Character formulae for queer Lie superalgebras and canonical bases of types $A/C$
• The primitive spectrum and category O for the periplectic Lie superalgebra
• Bott-Borel-Weil theory, BGG reciprocity and twisting functors for Lie superalgebras
• Characters of (relatively) integrable modules over affine Lie superlagebras
• Annihilator ideals and blocks of Whittaker modules over quasireductive Lie superalgebras
• Parabolic category ${\mathcal{O}}^{\mathfrak{p}}$ for periplectic Lie superalgebras $\mathfrak{pe}(n)$
• Whittaker coinvariants for $\mathrm{GL}(m|n)$
• Simple supermodules over Lie superalgebras
• Some homological properties of category $\mathcal{O}$ for Lie superalgebras
• Blocks and characters of $G(3)$-modules of non-integral weights
• Quantum group of type $A$ and representations of queer Lie superalgebra
• On semisimplicity of Jantzen middles for the periplectic Lie superalgebra