Something weird is definitely happening because...

Non-secure links to the invites, such as http://gmail.google.com/gmail/<invite_code_here> work for me in IE

Secure links to the invites, such as https://gmail.google.com/gmail/<invite_code_here> do not work in IE

Neither secure nor unsecure links to any parent page work in IE.

All links work in firefox.

Someone please shoot me now.
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Tony Fabris