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[ACR18] Achar, Pramod N.; Cooney, Nicolas; Riche, Simon The parabolic exotic t-structure, Épijournal de Géom. Algébr., EPIGA, Volume 2 (2018), 8, 31 pages | MR | Zbl

[AJS94] Andersen, Henning H.; Jantzen, Jens C.; Soergel, Wolfgang Representations of quantum groups at a $p$-th root of unity and of semisimple groups in characteristic $p$: independence of $p$, Astérisque, 220, Société Mathématique de France, 1994 | Numdam | Zbl

[AMRW19] Achar, Pramod N.; Makisumi, Shotaro; Riche, Simon; Williamson, Geordie Koszul duality for Kac–Moody groups and characters of tilting modules, J. Am. Math. Soc., Volume 32 (2019) no. 1, pp. 261-310 | DOI | MR | Zbl

[And98] Andersen, Henning H. Tilting modules for algebraic groups, Algebraic groups and their representations (Cambridge, 1997) (NATO ASI Series. Series C. Mathematical and Physical Sciences), Volume 517, Kluwer Academic Publishers, 1998, pp. 25-42 | DOI | MR | Zbl

[AR19] Achar, Pramod N.; Riche, Simon Dualité de Koszul formelle et théorie des représentations modulaire des groupes algébriques réductifs, SMF 2018 : Congrès de la Société Mathématique de France (Séminaires et Congrès), Volume 33, Société Mathématique de France (2019), pp. 83-172 | Zbl

[BBM04] Bezrukavnikov, Roman; Braverman, Alexander; Mirković, Ivan Some results about geometric Whittaker model, Adv. Math., Volume 186 (2004) no. 1, pp. 143-152 | DOI | MR | Zbl

[BGM + 19] Bezrukavnikov, Roman; Gaitsgory, Dennis; Mirković, Ivan; Riche, Simon; Rider, Laura An Iwahori–Whittaker model for the Satake category, J. Éc. Polytech., Math., Volume 6 (2019), pp. 707-735 | DOI | Numdam | MR | Zbl

[BNPS20] Bendel, Christopher P.; Nakano, Daniel K.; Pillen, Cornelius; Sobaje, Paul Counterexamples to the tilting and $(p,r)$-filtration conjectures, J. Reine Angew. Math., Volume 767 (2020), pp. 193-202 | DOI | MR | Zbl

[BY13] Bezrukavnikov, Roman; Yun, Zhiwei On Koszul duality for Kac–Moody groups, Represent. Theory, Volume 17 (2013), pp. 1-98 | DOI | MR | Zbl

[Don93] Donkin, Stephen On tilting modules for algebraic groups, Math. Z., Volume 212 (1993) no. 1, pp. 39-60 | DOI | MR | Zbl

[Fie10] Fiebig, Peter Lusztig’s conjecture as a moment graph problem, Bull. Lond. Math. Soc., Volume 42 (2010) no. 6, pp. 957-972 | DOI | MR | Zbl

[Fie11] Fiebig, Peter Sheaves on affine Schubert varieties, modular representations, and Lusztig’s conjecture, J. Am. Math. Soc., Volume 24 (2011) no. 1, pp. 133-181 | DOI | MR | Zbl

[Fie12] Fiebig, Peter An upper bound on the exceptional characteristics for Lusztig’s character formula, J. Reine Angew. Math., Volume 673 (2012), pp. 1-31 | DOI | MR | Zbl

[Hum71] Humphreys, James E. Modular representations of classical Lie algebras and semisimple groups, J. Algebra, Volume 19 (1971), pp. 51-79 | DOI | MR | Zbl

[IM65] Iwahori, Nagayoshi; Matsumoto, Hideya On some Bruhat decomposition and the structure of the Hecke rings of $𝔭$-adic Chevalley groups, Publ. Math., Inst. Hautes Étud. Sci., Volume 25 (1965), pp. 5-48 | DOI | Numdam | Zbl

[Jan80] Jantzen, Jens C. Darstellungen halbeinfacher Gruppen und ihrer Frobenius–Kerne, J. Reine Angew. Math., Volume 317 (1980), pp. 157-199 | MR | Zbl

[Jan03] Jantzen, Jens C. Representations of algebraic groups, Mathematical Surveys and Monographs, 107, American Mathematical Society, 2003 | Zbl

[JMW14] Juteau, Daniel; Mautner, Carl; Williamson, Geordie Parity sheaves, J. Am. Math. Soc., Volume 27 (2014) no. 4, pp. 1169-1212 | DOI | MR | Zbl

[JMW16] Juteau, Daniel; Mautner, Carl; Williamson, Geordie Parity sheaves and tilting modules, Ann. Sci. Éc. Norm. Supér., Volume 49 (2016) no. 2, pp. 257-275 | DOI | MR | Zbl

[JW17] Jensen, Lars T.; Williamson, Geordie The $p$-canonical basis for Hecke algebras, Categorification and higher representation theory (Beliakova, Anna et al., eds.) (Contemporary Mathematics), Volume 683, American Mathematical Society, 2017, pp. 333-361 | DOI | MR | Zbl

[KL93a] Kazhdan, David; Lusztig, George Tensor structures arising from affine Lie algebras I, J. Am. Math. Soc., Volume 6 (1993) no. 4, pp. 905-947 | DOI | MR | Zbl

[KL93b] Kazhdan, David; Lusztig, George Tensor structures arising from affine Lie algebras II, J. Am. Math. Soc., Volume 6 (1993) no. 4, pp. 949-1011 | DOI | Zbl

[KL94a] Kazhdan, David; Lusztig, George Tensor structures arising from affine Lie algebras III, J. Am. Math. Soc., Volume 7 (1994) no. 2, pp. 335-381 | DOI | MR | Zbl

[KL94b] Kazhdan, David; Lusztig, George Tensor structures arising from affine Lie algebras IV, J. Am. Math. Soc., Volume 7 (1994) no. 2, pp. 383-453 | DOI | MR | Zbl

[KT95] Kashiwara, Masaki; Tanisaki, Toshiyuki Kazhdan–Lusztig conjecture for affine Lie algebras with negative level, Duke Math. J., Volume 77 (1995) no. 1, pp. 21-62 | MR | Zbl

[KT96] Kashiwara, Masaki; Tanisaki, Toshiyuki Kazhdan–Lusztig conjecture for affine Lie algebras with negative level II: Non-integral case, Duke Math. J., Volume 84 (1996) no. 3, pp. 771-813 | Zbl

[Lus80a] Lusztig, George Hecke algebras and Jantzen’s generic decomposition patterns, Adv. Math., Volume 37 (1980), pp. 121-164 | DOI | MR | Zbl

[Lus80b] Lusztig, George Some problems in the representation theory of finite Chevalley groups, The Santa Cruz Conference on Finite Groups (Proceedings of Symposia in Pure Mathematics), Volume 37, American Mathematical Society (1980), pp. 313-317 | DOI | MR | Zbl

[Lus94] Lusztig, George Monodromic systems on affine flag manifolds, Proc. R. Soc. Lond., Volume 445 (1994) no. 1923, pp. 231-246 Errata in Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences vol. 450, (1995), 731–732 | MR | Zbl

[MR18] Mautner, Carl; Riche, Simon Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirković–Vilonen conjecture, J. Eur. Math. Soc., Volume 20 (2018) no. 9, pp. 2259-2332 | DOI | Zbl

[Ric] Riche, Simon Geometric Representation Theory in positive characteristic (habilitation thesis, available at https://tel.archives-ouvertes.fr/tel-01431526)

[RW18] Riche, Simon; Williamson, Geordie Tilting modules and the $p$-canonical basis, Astérisque, 397, Société Mathématique de France, 2018 | Zbl

[RW20] Riche, Simon; Williamson, Geordie Smith–Treumann theory and the linkage principle (2020) (https://arxiv.org/abs/2003.08522)

[Sob20] Sobaje, Paul On character formulas for simple and tilting modules, Adv. Math., Volume 369 (2020), 107172 | MR

[Soe97] Soergel, Wolfgang Kazhdan–Lusztig polynomials and a combinatorics for tilting modules, Represent. Theory, Volume 1 (1997), pp. 83-114 | DOI | MR | Zbl

[Spr82] Springer, Tonny A. Quelques applications de la cohomologie d’intersection, Séminaire N. Bourbaki, Vol. 1981/82 (Astérisque), Volume 92–93, Springer, 1982, pp. 249-273 | Numdam | Zbl

[Wil17] Williamson, Geordie Schubert calculus and torsion explosion, J. Am. Math. Soc., Volume 30 (2017) no. 4, pp. 1023-1046 | DOI | MR | Zbl