# What are defining & fundamental representations?

In physics terminology, one hears of the fundamental & defining representations of lie algebras or groups - are these the same as irreducible representations?

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On the other hand, the defining representations refer to Lie algebras that are defined as matrix subalgebras of $\mathfrak{gl}(n)$ (in which case the defining rep is on $\mathbb C^n$). For example, the defining representation of $\mathfrak{so}(n)$ is on $\mathbb C^n$ because $\mathfrak{so}(n)$ is defined as the space of skew-symmetric $n\times n$ matrices and these, by definition, act on $\mathbb C^n$.
For $\mathfrak{so}(n), \mathfrak{su}(n)$ and $\mathfrak{sp}(n)$, the defining representation is a fundamental representation (but of course there will be more fundamental representations).