Prior density for B-SVAR

Dear all,
I’m reading the paper by Waggoner and Zha (2003, JEDC). A working paper version of this paper can be found at this address: []
I have some troubles in deriving the prior in equation 7, when there are restrictions on the lagged coefficients. Can someone help me, with a sketch of proof?
I hope this is not off-topic question for this forum (even though I know that, In Dynare, this prior is implemented in MS-BVAR portions of codes).
Best regards,