In Georgi(Lie Algebras-Second Edition), theorem 1.5 states:(adsbygoogle = window.adsbygoogle || []).push({});

" The matrix elements of the unitary, irreducible representations of G are a complete orthonormal set for the vector space of the regular representation, or alternatively, for functions of g belonging to G."

Now, just before that, he says that the matrix elements of the regular representation can be written as linear combination of matrix elements of irreducible representations. Well...I imagine that the regular representation can be brought into block diagonal form by a similarity transformation such that each block represents some irreducible representation....Since the similarity transformation just mixes up the elements of a matrix, the matrix elements of regular rep are linear combination of the elements of the irreps.....this I understand...am happy!!

But what does he mean by vector space above? If he just means the elements of the matrices, I am happy and can understand......but I imagine the vector space to be the space of column vectors...you know..like...made of [tex]$\left(\begin{array}{c}

1\\

0\end{array}\right)$[/tex] and [tex]$\left(\begin{array}{c}

0\\

1\end{array}\right)$[/tex]

for SU(2)...

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Doubt from Georgi(Lie Algebras)

Loading...

Similar Threads for Doubt Georgi Algebras | Date |
---|---|

I Adding a matrix and a scalar. | Mar 31, 2018 |

I Doubt about proof on self-adjoint operators. | Nov 11, 2017 |

Doubt about condition solutions of complex line equation | Dec 10, 2014 |

Doubt about rotation isometry on the complex plane | Nov 14, 2014 |

When showing a super simple property about norms, I have a doubt about how much I can assume | Sep 25, 2014 |

**Physics Forums - The Fusion of Science and Community**