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Everything about Modular representation theory

Representation theory of finite groups over fields of positive characteristic

In mathematics, modular representation theory is the part of representation theory that studies linear representations of finite groups over fields of positive characteristic. As well as having applications to group theory, modular representations arise naturally in other branches of mathematics, such as algebraic geometry, number theory and combinatorics. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Modular representation theoryA 5-minute orientation
  2. Skim a recent paper: Assembly Configuration Representation and Kinematic Modeling for Modular Reconfigurable Robots Based on Graph TheoryInfluential work since 2022
  3. Pick up a classic book: Representation theory of finite groups and associative algebrasThe most-reprinted book on the subject
  4. Read the landmark paper: Modular and conformal invariance constraints in representation theory of affine algebrasCited 179 times
  5. Go sideways: Brauer's three main theoremsA closely related topic
  6. Go sideways: Brauer–Nesbitt theoremA closely related topic

📖 Definitions

No dictionary entry for this exact phrase.

🗂️ The subject at a glance

  1. History
  2. Example
  3. Ring theory interpretation
  4. Brauer characters
  5. Reduction (mod p)
  6. Number of simple modules
  7. Blocks and the structure of the group algebra
  8. Projective modules
  9. Some orthogonality relations for Brauer characters
  10. Decomposition matrix and Cartan matrix
  11. Defect groups

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics