The Dynkin index of a representation fixes the trace normalization up to the convention for the generators. It controls matter contributions to gauge beta functions and mixed anomalies.
The cubic anomaly coefficient is defined by the symmetrized trace of three representation matrices. A conjugate representation has the opposite coefficient, while a real or pseudoreal representation has coefficient zero.
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The Dynkin index, also known as the Dynkin index of a representation, is a concept that arises in the study of Lie algebras and Lie groups, particularly in the context of representation theory. It provides a way to quantify the degree of "mixing" or "interaction" of a representation with the structure of the algebra, especially when considering the space of invariant functions or the geometry associated with the representation.