Geometric Representation Theory
Flag varieties, D-modules, and the Beilinson–Bernstein localization.
Geometric Representation Theory. Flag varieties, D-modules, and the Beilinson–Bernstein localization.
Foundations and canonical references
The standard treatments of geometric representation theory approach the subject from complementary angles. Chriss, Representation Theory and Complex Geometry (1997) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Hotta, D-Modules, Perverse Sheaves, and Representation Theory (2008) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.
Open methodological questions for geometric representation theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1997Representation Theory and Complex Geometrychriss-1997, ginzburg-1997
- textbook · supporting · 2008D-Modules, Perverse Sheaves, and Representation Theoryhotta-2008, takeuchi-2008, tanisaki-2008
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