Representation theory

Chang number

In mathematics, the Chang number of an irreducible representation of a simple complex Lie algebra is its dimension modulo 1 + h, where h is the Coxeter number. Chang numbers are named after , who rediscovered an element of order h + 1 found by . showed that there is a unique class of regular elements σ of order h + 1, in the complex points of the corresponding Chevalley group. He showed that the trace of σ on an irreducible representation is −1, 0, or +1, and if h + 1 is prime then the trace is congruent to the dimension mod h+1. This implies that the dimension of an irreducible representation is always −1, 0, or +1 mod h + 1 whenever h + 1 is prime. (Wikipedia).

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Dividing Complex Numbers Example Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys

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From playlist Complex Numbers

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Related pages

Lie algebra | G2 (mathematics) | Lie group