Projective modules over classical Lie algebras of infinite rank in the parabolic category

@article{Chen2018ProjectiveMO,
  title={Projective modules over classical Lie algebras of infinite rank in the parabolic category},
  author={Chih-Whi Chen and Ngau Lam},
  journal={Journal of Pure and Applied Algebra},
  year={2018}
}
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4 Citations

4 Citations

GRADED SUPER DUALITY FOR GENERAL LINEAR LIE SUPERALGEBRAS

We provide a new proof of the super duality equivalence between infinite-rank parabolic BGG categories of general linear Lie (super) algebras conjectured by Cheng and Wang and first proved by Cheng…

GRADED SUPER DUALITY FOR GENERAL LINEAR LIE SUPERALGEBRAS

We provide a new proof of the super duality equivalence between infinite-rank parabolic BGG categories of general linear Lie (super) algebras conjectured by Cheng and Wang and first proved by Cheng…

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37 References

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Review of semisimple Lie algebras Highest weight modules: Category $\mathcal{O}$: Basics Characters of finite dimensional modules Category $\mathcal{O}$: Methods Highest weight modules I Highest…

GRADED SUPER DUALITY FOR GENERAL LINEAR LIE SUPERALGEBRAS

We provide a new proof of the super duality equivalence between infinite-rank parabolic BGG categories of general linear Lie (super) algebras conjectured by Cheng and Wang and first proved by Cheng…

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

Highest weight categories arising from Khovanov's diagram algebra III: category O

We prove that integral blocks of parabolic category O associated to the subalgebra gl(m) x gl(n) of gl(m+n) are Morita equivalent to quasi-hereditary covers of generalised Khovanov algebras. Although…

Some homological properties of category O. III

We prove that thick category $\mathcal{O}$ associated to a semi-simple complex finite dimensional Lie algebra is extension full in the category of all modules. We also prove the weak Alexandru…

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We apply the super duality formalism recently developed by the authors to obtain new equivalences of various module categories of general linear Lie superalgebras. We establish the correspondence of…

KOSZUL DUALITY FOR PARABOLIC AND SINGULAR CATEGORY O

This paper deals with a generalization of the “Koszul duality theorem” for the Bernstein-Gelfand-Gelfand category O over a complex semisimple Lie-algebra, established by Beilinson, Ginzburg and…

Irreducible Characters of General Linear Superalgebra and Super Duality

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating…

Super Duality and Homology of Unitarizable Modules of Lie Algebras

The u-homology formulas for unitarizable modules at negative levels over classical Lie algebras of infinite rank of types gl(n), sp(2n) and so(2n) are obtained. As a consequence, we recover the…

Tensor product categorifications and the super Kazhdan-Lusztig conjecture

We give a new proof of the "super Kazhdan-Lusztig conjecture" for the Lie super algebra $\mathfrak{gl}_{n|m}(\mathbb{C})$ as formulated originally by the first author. We also prove for the first…