D-modules, perverse sheaves, and representation theory.
D-modules bridge many different areas of mathematics, including Algebraic and Differential Geometry, Complex Analysis, Category Theory, Differential Equations, and Representation Theory. “D-modules, perverse sheaves, and representation theory” is an expanded translation of a Japanese monograph of Ryoshi Hotta, Kiyoshi Takeuchi and Toshiyuki Tanisaki. As the review of Gheorge Gussi [Zbl 1136.14009] points out:
“The aim of this book is to give a comprehensive introduction to D-modules (mainly on algebraic varieties) and the application of this theory to representation theory. The exposition culminates with the proof of two important theorems, i.e. of the Riemann-Hilbert correspondence (in the first part) and the proof of the Kazhdan-Lusztig conjecture (in the second part). While there are some excellent texts on D-modules, this is the first systematic presentation on representation theory in connection with D-modules. Since now the theory of D-modules has attained a high degree of maturity, the first part is an excellent introduction.”