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Communications in Algebra Volume 32, 2004 - Issue 6
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Original Articles

Tilting Modules for Lie Superalgebras

Jonathan Brundan Department of Mathematics, University of Oregon, Eugene, Oregon, USA; Department of Mathematics, University of Oregon, Eugene, OR, 97403-1222, USACorrespondence[email protected]
Pages 2251-2268 | Received 01 Nov 2002, Published online: 18 Aug 2006
 
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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.

Mathematics Subject Classification:

Acknowledgment

The work is partially supported by the NSF (grant no. DMS-0139019).

Notes

#Communicated by B. Parshall.

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