Introduction to Soergel Bimodules (Paperback)

- Part I The Classical Theory of Soergel Bimodules. - How to Think About Coxeter Groups. - Reflection Groups and Coxeter Groups. - The Hecke Algebra and Kazhdan?Lusztig Polynomials. - Soergel Bimodules. - The “Classical” Theory of Soergel Bimodules. - Sheaves on Moment Graphs. - Part II Diagrammatic Hecke Category. - How to Draw Monoidal Categories. - Frobenius Extensions and the One-Color Calculus. - The Dihedral Cathedral. - Generators and Relations for Bott?Samelson Bimodules and the Double Leaves Basis. - The Soergel Categorification Theorem. - How to Draw Soergel Bimodules. - Part III Historical Context: Category O and the Kazhdan?Lusztig Conjectures. - Category O and the Kazhdan?Lusztig Conjectures. - Lightning Introduction to Category O. - Soergel’s V Functor and the Kazhdan?Lusztig Conjecture. - Lightning Introduction to Perverse Sheaves. - Part IV The Hodge Theory of Soergel Bimodules - Hodge Theory and Lefschetz Linear Algebra. - The Hodge Theory of Soergel Bimodules. - Rouquier Complexes and Homological Algebra. - Proof of the Hard Lefschetz Theorem. - Part V Special Topics. - Connections to Link Invariants. - Cells and Representations of the Hecke Algebra in Type A. - Categorical Diagonalization. - Singular Soergel Bimodules and Their Diagrammatics. - Koszul Duality I. - Koszul Duality II. - The p-Canonical Basis.