Tilting Modules for Lie Superalgebras
By Jonathan Brundan. 2002
65 citations recorded by the source corpus.
Abstract We develop a general theory of tilting modules for graded Lie superalgebras, extending work of Soergel for graded Lie algebras. The main result of the article gives a twisted version of BGG reciprocity relating multiplicities in Δ-flags of indecomposable tilting modules to composition multiplicities of costandard modules. We then discuss the examples 𝔤l(m|n) and 𝔮(n) in detail.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b1eb8c0c8c7be8dca83583ef348e12b2e1e20caf
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In Algebra and Number Theory
- Ben Webster
- C. Stroppel
- Jonathan Brundan
- I. Losev
- Aaron D. Lauda
- Mikhail Khovanov
- Alexander S. Kleshchev
- Volodymyr Mazorchuk
In Geometry and Topology
- Ben Webster
- C. Stroppel
- Jonathan Brundan
- I. Losev
- Aaron D. Lauda
- Mikhail Khovanov
- Alexander S. Kleshchev
- Raphaël Rouquier
In Statistical and Nonlinear Physics
- C. Stroppel
- Jonathan Brundan
- Ben Webster
- I. Losev
- Mikhail Khovanov
- Joshua Sussan
- Aaron D. Lauda
- Alexander S. Kleshchev
Citations in the corpus
- Tensor product categorifications and the super Kazhdan-Lusztig conjecture (2013, background): “e bottom and other sections of the form qn∆(µ) for µ<λand n∈Z. The existence of such an object follows by a construction due to Ringel involving taking iterated extensions of standard objects; cf. [B2] which justifies in the context of super parabolic category Othat Ringel’s construction terminate”
- Highest weight categories arising from Khovanov's diagram algebra IV: the general linear supergroup (2009, background): “By [Z] or the discussion in [ B2 , Example 7.5], the category of all nite dimensional G-modules has enough projectives.”