• 1 Td Groups ▶
    • 1.1 Definitions
    • 1.2 Example: \(\mathrm{GL}_n(K)\) and Its Closed Subgroups
  • 2 Continuous Representations of Groups with Topology ▶
    • 2.1 Continuous representations
    • 2.2 The category of continuous representations
  • 3 The Hecke Algebra of a Td Group ▶
    • 3.1 Locally constant functions and distributions on a td space ▶
      • 3.1.1 Extension by zero and restriction
    • 3.2 Distributions on groups ▶
      • 3.2.1 Translations of functions
      • 3.2.2 Compactly supported distributions and convolution
      • 3.2.3 Translation actions on distributions
      • 3.2.4 Delta distributions and a normalized Haar distribution
      • 3.2.5 Convolution identities for delta and normalized Haar distributions
      • 3.2.6 Invariance of the normalized Haar distribution
      • 3.2.7 Finite decomposition for bi-invariant distributions
      • 3.2.8 Local constancy (smoothness)
    • 3.3 The Hecke algebra
    • 3.4 TODOs
  • Dependency graph

\(p\)-adic Representation Theory (PadicRep)

Shurui Liu, Zhuoni Chi

Our goal is to formalize basics of \(p\)-adic representation theory.

Currently, we focus on \(\mathbb {C}\)-representations of \(p\)-adic groups.

  • 1 Td Groups
    • 1.1 Definitions
    • 1.2 Example: \(\mathrm{GL}_n(K)\) and Its Closed Subgroups
  • 2 Continuous Representations of Groups with Topology
    • 2.1 Continuous representations
    • 2.2 The category of continuous representations
  • 3 The Hecke Algebra of a Td Group
    • 3.1 Locally constant functions and distributions on a td space
      • 3.1.1 Extension by zero and restriction
    • 3.2 Distributions on groups
      • 3.2.1 Translations of functions
      • 3.2.2 Compactly supported distributions and convolution
      • 3.2.3 Translation actions on distributions
      • 3.2.4 Delta distributions and a normalized Haar distribution
      • 3.2.5 Convolution identities for delta and normalized Haar distributions
      • 3.2.6 Invariance of the normalized Haar distribution
      • 3.2.7 Finite decomposition for bi-invariant distributions
      • 3.2.8 Local constancy (smoothness)
    • 3.3 The Hecke algebra
    • 3.4 TODOs