What would you like to understand?

Relabeling the blocks by inequivalent irreducible representations groups equivalent irreducible summands under a single label. This makes it possible to introduce a multiplicity number $a_j$ that records how many times the irreducible representation $\Gamma^j$ occurs in $\Gamma$, leading to the compact expression $\Gamma = \bigoplus_j a_j \Gamma^j$.

Conditions: The original block diagonal decomposition is available.; Equivalent irreducible summands are grouped under the same label.

Relabeling the blocks by inequivalent irreducible representations groups equivalent irreducible summands under a single label. This makes it possible to introduce a multiplicity number $a_j$ that records how many times the irreducible representation $\Gamma^j$ occurs in $\Gamma$, leading to the compact expression $\Gamma = \bigoplus_j a_j \Gamma^j$.

Conditions: The original block diagonal decomposition is available.; Equivalent irreducible summands are grouped under the same label.