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Everything is over an algebraically closed field of characteristic $\neq 2$. I had constructed a root datum for $\textrm{GSp}_4$ in a less than ideal way, and I had hoped to show that it was self ...

For the root system of the type $A_n$, the roots are $\alpha _{i,j}$, $1\le i\neq j\le n$, we have the nontrivial relations $(x_{i,j} (t), x_{j,k}(u)) = x_{i,k}(tu)$ if $i, j, k$ are distinct. ($x_{i,...