What is the dimension of Borel subgroup of $Sp(2n,\mathbb C) $ ?
I know that if I choose the bilinear form nicely then Borel subgroup of $Sp(2n,\mathbb C)$ is just the intersection $Sp(2n,\mathbb C) \cap T(2n,\mathbb C)$, where $T(2n,\mathbb C)$ is the set of upper triangular invertible matrices. In this scenario, my calculation shows that the dimension should be $n^2 + \dfrac{n(n+1)}{2}$. Is it correct ?