Lectures on Algebraic Categorification

  • Volodymyr Mazorchuk

    Uppsala University, Sweden
Lectures on Algebraic Categorification cover
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FrontmatterDownload pp. i–iv
PrefaceDownload p. v
ContentsDownload pp. vii–ix
1Basics: decategorification and categorificationpp. 1–7
2Basics: from categorification of linear maps to 2-categoriespp. 9–15
3Basics: 2-representations of finitary 2-categoriespp. 17–23
4Category O\mathcal{O}: definitionspp. 25–32
5Category O\mathcal{O}: projective and shuffling functorspp. 33–39
6Category O\mathcal{O}: twisting and completionpp. 41–46
7Category O\mathcal{O}: grading and combinatoricspp. 47–53
8Sn\mathbb{S}_n-categorification: Soergel bimodules, cells and Specht modulespp. 55–60
9Sn\mathbb{S}_n-categorification: (induced) cell modulespp. 61–66
10Category O\mathcal{O}: Koszul dualitypp. 67–73
11sl2\mathfrak{sl}_2-categorification: simple finite-dimensional modulespp. 75–80
12Application: categorification of the Jones polynomialpp. 81–86
13sl2\mathfrak{sl}_2-categorification of Chuang and Rouquierpp. 87–92
14Application: blocks of F[Sn]\mathbb{F}[\mathbb{S}_n] and Broué’s conjecturepp. 93–98
15Applications of Sn\mathbb{S}_n-categorificationspp. 99–104
16Exercisespp. 105–107
Bibliographypp. 109–115
Indexpp. 117–119