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COMPARISON OF CANONICAL BASES FOR SCHUR AND UNIVERSAL ENVELOPING ALGEBRAS

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Abstract

We show that the canonical bases in and the Schur algebra are compatible; in fact we extend this result to p-canonical bases. This follows immediately from a fullness result for a functor categorifying this map. In order to prove this result, we also explain the connections between categorifications of the Schur algebra which arise from parity sheaves on partial ag varieties, singular Soergel bimodules and Khovanov and Lauda's “flag category," which are of some independent interest.

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Authors and Affiliations

  1. Department of Mathematics, University of Virginia, Charlottesville, VA, USA

    BEN WEBSTER

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  1. BEN WEBSTER
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Correspondence to BEN WEBSTER.

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*Supported by the NSF under Grant DMS-1151473 and the Alfred P. Sloan Foundation.

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WEBSTER, B. COMPARISON OF CANONICAL BASES FOR SCHUR AND UNIVERSAL ENVELOPING ALGEBRAS. Transformation Groups 22, 869–883 (2017). https://doi.org/10.1007/s00031-016-9409-2

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  • DOI: https://doi.org/10.1007/s00031-016-9409-2

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