Koszul dual 2-functors and extension algebras of simple modules for $GL_2$

Vanessa Miemietz; Will Turner

Koszul dual 2-functors and extension algebras of simple modules for $GL_2$

Representation Theory 2014-07-10 v3

Authors: Vanessa Miemietz , Will Turner

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.

Keywords

Koszul duality 2-functors Yoneda extension algebra GL_2 rational representations characteristic p

Cite

@article{arxiv.1106.5411,
  title  = {Koszul dual 2-functors and extension algebras of simple modules for $GL_2$},
  author = {Vanessa Miemietz and Will Turner},
  journal= {arXiv preprint arXiv:1106.5411},
  year   = {2014}
}

Comments

39 pages, title changed in second version, to appear in Selecta Math. (N.S.)

Koszul dual 2-functors and extension algebras of simple modules for $GL_2$

Abstract

Keywords

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