My question is how to find the Iwasawa Decomposition of $Gsp_n=\{g\in GL_{2n}:g^tJg=\mu(g)J, \mu(g) \mathrm{is\ a\ constant}\}$, where $J=\left(\begin{array}{cc} & I_n \\ -I_n & \end{array} \right)$?

And I am also really confused about how to find the Iwasawa decomposition for the general cases, it would be appreciated if you could offer some guidance or some accessible reference. Thanks!


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