Irreducible representations (irreps) | Representation theory episode 3 скачать в хорошем качестве

Irreducible representations (irreps) | Representation theory episode 3

Exclusive content on Patreon: https://www.patreon.com/user?u=86649007 #grouptheory #linearalgebra #matrices #representationtheory Matrix representations are one of the most important tools in modern physics. But any given group has infinitely many matrix representations, so we want to organize them by breaking them into smaller pieces. We look at the smallest possible pieces, which are called irreducible representations. They act like the prime numbers. Just like any number can be constructed from primes, any representation can be constructed from irreducible ones. Many thanks to professor Karel Dekimpe from the university of Leuven for helping me understand representations and characters. Don't forget to check out these links: [PENN 1]    • Representations of Finite Groups | Definit...   Michael Penn looks at simple representations for some small groups. In the second half of the video, he looks at the cyclic groups, and he explains why we keep finding complex roots of unity. [PENN 2]    • Representations of Finite Groups | A few m...   Michael Penn looks at more examples of group representations, specifically for non-abelian groups. He shows how to extend representations for a cyclic group to a dihedral group. He also talks about the quaternion group. This should give you a good initial idea of how difficult it can be to find representations for non-commutative groups in general. 0:00 Composing bigger representations from smaller ones 1:25 Decomposing the cyclic group with 2 elements 2:38 A simple eigenvector for all permutation matrices 8:25 Irreducible representations are like prime numbers 10:50 A bigger example: the cyclic group with 4 elements 12:39 Placing restrictions on the smaller representations 17:45 Decomposing the geometric representation 18:58 Cyclic and abelian groups in general 20:52 The regular representation is a catalog This video is published under a CC Attribution license ( https://creativecommons.org/licenses/... )