  We discuss the ground-state degeneracy of spin-$1/2$ kagome-lattice quantum
antiferromagnets on magnetization plateaus by employing two complementary
methods: the adiabatic flux insertion in closed boundary conditions and a 't
Hooft anomaly argument on inherent symmetries in a quasi-one-dimensional limit.
The flux insertion with a tilted boundary condition restricts the lower bound
of the ground-state degeneracy on $1/9$, $1/3$, $5/9$, and $7/9$ magnetization
plateaus under the $\mathrm{U(1)}$ spin-rotation and the translation
symmetries: $3$, $1$, $3$, and $3$, respectively. This result motivates us
further to develop an anomaly interpretation of the $1/3$ plateau. Taking
advantage of the insensitivity of anomalies to spatial anisotropies, we examine
the existence of the unique gapped ground state on the $1/3$ plateau from a
quasi-one-dimensional viewpoint. In the quasi-one-dimensional limit, kagome
antiferromagnets are reduced to weakly coupled three-leg spin tubes. Here, we
point out the following anomaly description of the $1/3$ plateau. While a
simple $S=1/2$ three-leg spin tube cannot have the unique gapped ground state
on the $1/3$ plateau because of an anomaly between a $\mathbb Z_3\times \mathbb
Z_3$ symmetry and the translation symmetry at the $1/3$ filling, the kagome
antiferromagnet breaks explicitly one of the $\mathbb Z_3$ symmetries related
to a $\mathbb Z_3$ cyclic transformation of spins in the unit cell. Hence the
kagome antiferromagnet can have the unique gapped ground state on the $1/3$
plateau.
