The invariants algebra for the action of $Sp(2m)$ in $\bigotimes\limits^\infty M_{2m}\mathbb{C}$

Methods introduced by the author and A. M. Vershik are used to compute the traces and the dimensions group of the subalgebra of $Sp(2m)$-invariants in $\bigotimes\limits^\infty M_{2m}\mathbb{C}$.