nLab
representation theory

Related entries

• representation, action, module

  • group, group algebra, groupoid, algebraic group, Lie algebra

  • vector space, affine space, symplectic vector space

  • action, module, equivariant object

  • bimodule, Morita equivalence, induced representation

  • Hilbert space, Banach space, Fourier transform, functional analysis

  • weight (in representation theory)

  • orbit, coadjoint orbit, Killing form

  • geometric quantization, coherent state

  • socle, quiver

  • module algebra, comodule algebra, Hopf action, measuring

• geometric representation theory

  • Borel-Weil theorem, Beĭlinson-Bernstein localization
  • D-module, perverse sheaf, BBDG decomposition theorem
  • Kazhdan-Lusztig theory

• Grothendieck group, lambda-ring, symmetric function, formal group

• principal bundle, torsor, vector bundle, Atiyah Lie algebroid

• geometric function theory, groupoidification

• Eilenberg-Moore category, algebra over an operad, actegory, crossed module

• reconstruction theorems

References

A list of texts on representation theory is maintained at

• Mikhail Khovanov, Resources.

The relation to number theory and the Langlands program is discussed in

• Robert Langlands, Representation theory: Its rise and its role in number theory (web)