= Tensor square of the defining C2 crystal
{title2=$B(\omega_1)^{\otimes2}=B(2\omega_1)\sqcup B(\omega_2)\sqcup B(0)$}
Under the <crystal tensor-product rule> that uses the first factor for lowering when $\varphi_i(a)>\varepsilon_i(b)$, the four-letter <C2 root system> crystal has highest tensor vertices $1\otimes1$, $1\otimes2$ and $1\otimes\bar1$. Their <highest weights> are $2\omega_1$, $\omega_2$ and zero. Lowering generates connected components of sizes ten, five and one, respectively; their union exhausts all sixteen vertices. The corresponding representation decomposition is the symmetric square plus the primitive exterior square and the invariant symplectic line.
Back to article page
