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The degenerate analogue of Ariki’s categorification theorem

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Abstract

We explain how to deduce the degenerate analogue of Ariki’s categorification theorem over the ground field \({\mathbb{C}}\) as an application of Schur–Weyl duality for higher levels and the Kazhdan–Lusztig conjecture in finite type A. We also discuss some supplementary topics, including Young modules, tensoring with sign, tilting modules and Ringel duality.

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Authors and Affiliations

  1. Department of Mathematics, University of Oregon, Eugene, OR, 97403, USA

    Jonathan Brundan & Alexander Kleshchev

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  1. Jonathan Brundan
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  2. Alexander Kleshchev
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Correspondence to Jonathan Brundan.

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Research supported in part by NSF grant no. DMS-0654147.

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Brundan, J., Kleshchev, A. The degenerate analogue of Ariki’s categorification theorem. Math. Z. 266, 877–919 (2010). https://doi.org/10.1007/s00209-009-0603-y

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