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Koszul duality of affine Kac-Moody algebras and cyclotomic rational double affine Hecke algebras

Raphaël Rouquier UCLA Peng Shan Tsinghua University Michela Varagnolo University of Cergy-Pontoise

Quantum Algebra Representation Theory mathscidoc:1908.29001

Advances in Mathematics, 262, 370-435, 2014
We give a proof of the parabolic/singular Koszul duality for the category O of affine Kac–Moodyalgebras. The main new tool is a relation between moment graphs and finite codimensional affine Schubert varieties. We apply this duality to q-Schur algebras and to cyclotomic rational double affine Heckealgebras.This yields a proof of a conjecture of Chuang–Miyachi relating the level-rank duality with the Ringel–Koszul duality of cyclotomic rational double affine Hecke algebras.
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@inproceedings{raphaël2014koszul,
  title={Koszul duality of affine Kac-Moody algebras and cyclotomic rational double affine Hecke algebras},
  author={Raphaël Rouquier, Peng Shan, and Michela Varagnolo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190828144151044777473},
  booktitle={Advances in Mathematics},
  volume={262},
  pages={370-435},
  year={2014},
}
Raphaël Rouquier, Peng Shan, and Michela Varagnolo. Koszul duality of affine Kac-Moody algebras and cyclotomic rational double affine Hecke algebras. 2014. Vol. 262. In Advances in Mathematics. pp.370-435. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190828144151044777473.
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