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This paper develops a general theory of canonical bases, and how they arise naturally in the context of categorification.
J. Brundan and A. Kleshchev, Graded decomposition numbers for cyclotomic Hecke algebras , Adv. Math. 222
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by same author, Canonical bases in tensor products , Proc. Nat. Acad. Sci. U.S.A. 89
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Wolfgang Soergel, The combinatorics of Harish-Chandra bimodules , J. Reine Angew. Math. 429
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Alexander Beilinson, Victor Ginzburg, and Wolfgang Soergel, Koszul duality patterns in representation theory , J. Amer. Math. Soc. 9
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Edward Cline, Brian Parshall, and Leonard Scott, Stratifying endomorphism algebras , Mem. Amer. Math. Soc. 124
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A. Lascoux, B. Leclerc, and J.-Y. Thibon, Hecke algebras at roots of unity and crystal bases of quantum affine algebras , Comm. Math. Phys. 181
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Jie Du, Brian Parshall, and Leonard Scott, Stratifying endomorphism algebras associated to Hecke algebras , J. Algebra 203
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D. Uglov, Canonical bases of higher-level q q -deformed Fock spaces and Kazhdan-Lusztig polynomials , Physical combinatorics (Kyoto, 1999), Progr. Math., vol. 191, Birkhäuser, 2000, pp. 249–299
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István Ágoston, Vlastimil Dlab, and Erzsébet Lukács, Quasi-hereditary extension algebras , Algebr. Represent. Theory 6
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S. Ariki, Graded q q -Schur algebras , 2009, arXiv: 0903.3453
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Jonathan Brundan and Alexander Kleshchev, Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras , Invent. Math. 178
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Peng Shan, Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras , Ann. Sci. Éc. Norm. Supér. (4) 44
2011
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Michela Varagnolo and Eric Vasserot, Canonical bases and KLR-algebras , J. Reine Angew. Math. 659
2011
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by same author, Hypertoric category 𝒪 \mathcal{O} , Adv. Math. 231
2012
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Masaki Kashiwara, Notes on parameters of quiver Hecke algebras , Proc. Japan Acad. Ser. A Math. Sci. 88
2012
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Seok-Jin Kang and Masaki Kashiwara, Categorification of highest weight modules via Khovanov-Lauda-Rouquier algebras , Invent. Math. 190
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Pramod N. Achar and Catharina Stroppel, Completions of Grothendieck groups , Bull. Lond. Math. Soc. 45
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