I am new to group theory, I can't understand, how to find orbits of adjoint representation of $SU(2)$ group. I appreciate any help, thank you in progress
2026-04-08 09:33:14.1775640794
Find orbits of SU(2) adjoint representation
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Hint: Try to think about linear algebra rather than group theory. The Lie algebra of $SU(2)$ consists of all skew-Hermitian matrices (i.e. matrices $X$ such that $X^*=-X$) and the adjoint action of $A$ maps $X$ to $AXA^{-1}$. Now think about what linear algebra tells you about looking at such matrices up to conjugation by a unitary matrix (i.e. up to the choices of an oriented orthonormal basis).