Geometric Quantization: Representation Theory

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Related lectures (27)

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Categorical Perspective: Group Actions

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

Rank Theorem: Part 2

Delves into the Rank Theorem's implications for linear transformations and mappings.

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Linear Algebra: Systems of Equations and Transformations

Explores systems of linear equations, transformations, dilatation, rotation, and cross ratios in linear algebra.

Generalization of Change of Basis Matrices

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Vector Spaces: Linear Applications and Generators

Introduces vector spaces, linear applications, generators, and dimensionality in mathematics.

Group Theory: Recalls

Offers a recap on group theory, focusing on linear applications and bases.

Lie Groups: SU(2) and SO(3)

Covers Lie groups, focusing on SU(2) and SO(3), discussing group structure and representations.

Group representations constructions

Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.

Group Actions: Differential of Orbit Map

Explores the differential of group actions on vector spaces and the behavior of orbit maps.