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Koszul dual \(2\)-functors and extension algebras of simple modules for \(GL_2\)

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Abstract

Let \(p\) be a prime number. We compute the Yoneda extension algebra of \(GL_2\) over an algebraically closed field of characteristic \(p\) by developing a theory of Koszul duality for a certain class of \(2\)-functors, one of which controls the category of rational representations of \(GL_2\) over such a field.

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Authors and Affiliations

  1. School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK

    Vanessa Miemietz

  2. Department of Mathematics, King’s College, University of Aberdeen, Fraser Noble Building, Aberdeen, AB24 3UE, UK

    Will Turner

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  1. Vanessa Miemietz
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  2. Will Turner
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Correspondence to Vanessa Miemietz.

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Miemietz, V., Turner, W. Koszul dual \(2\)-functors and extension algebras of simple modules for \(GL_2\) . Sel. Math. New Ser. 21, 605–648 (2015). https://doi.org/10.1007/s00029-014-0164-8

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  • DOI: https://doi.org/10.1007/s00029-014-0164-8

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