= B2 spin crystal
{c}
{title2=$B(\Lambda_2)$}
For the <B2 root system> with $\alpha_1=\varepsilon_1-\varepsilon_2$ long and $\alpha_2=\varepsilon_2$ short, the spin <fundamental weight> is $\Lambda_2=(\varepsilon_1+\varepsilon_2)/2$. Its four-dimensional <highest-weight representation> has the <minuscule weight> orbit $\tfrac12(\pm\varepsilon_1\pm\varepsilon_2)$, each of multiplicity one. The <crystal basis> is the chain $++\xrightarrow{2}+-\xrightarrow{1}-+\xrightarrow{2}--$, where signs denote the coordinates. Each <Kashiwara operator> subtracts its indicated simple root; the <sl2 Lie algebra> strings have length one. This fixes every edge and gives a connected highest-weight graph with the correct character.
Back to article page
