Representation Theory

Please find linked

• Jun 12, 2021 06:29 AM . Som Phene . Mahadevan Subramanian . Vaishnav Rao . Prakhar Patel . Pandurang Deore - SoS, IITB Meeting Recording - Representation Theory I
• Jun 12, 2021 06:29 AM . Som Phene . Mahadevan Subramanian . Vaishnav Rao . Prakhar Patel . Pandurang Deore - SoS, IITB Meeting - Representation Theory Note I
• Quantum Field Theory: Symmetry, Circuit, Branching
• Classical Field Theory: Interaction, Electrodynamics, Formulation
• Combinatorics: Counting by uniform distribution, Entropy, expectation
• Logic: Axiom, Recursive, Complete, Uniform, Existence, Game
  • Group is Symmetry
• Knowledge is ignorance (symmetries that we willingly go blind to).

Group

• Set closed under associative binary operation with identity and inverse element
• Var
  • Page Zoom in or out, composition
  • Page scroll up or down, composition
  • Integers, addition
  • Rotation \(SO(3)\), composition
• Relate Sigma Algebra

Graph

• State, interaction
• vertex, edge
• Adjacency Matrix is symmetric, Diagonal matrix is mirror
• Adjacency matrix composition counts walks on graph
• Spectral Theorem identifies Real Symmetric Matrix to the Diagonal matrix: real eigenvalue, orthonormal eigenvector basis
• Cycles on graph correspond to Eigenvalue

Classify Interaction

• Quiver to RefDigraph isomorphic ColDigraph Category
• (Gabriel) Quiver (Directed graph) is of finite type if and only if underlying graph is \(A_n or D_n or E_6 or E_7 or E_8\) Dynkin diagram, with indecomposable representation corresponding to positive root.