@johncarlosbaez Hi John! Please feel free to use my post however you want, with any attribution or no attribution at all, anything is okay with me. Here I usually go by "mist" (I change my display name from time to time, but it's always a pun on 'mist')
Yes, I did mean to include t > 0, thanks for the correction. I've edited my post accordingly
I also found another error: in the last paragraph, the action on the horosphere slice is given by simple reflections e_1, e_2, e_3, NOT by the simple reflections e_2, e_3, e_4. I used a different numbering on my scratch paper and copied it over incorrectly. I've edited to fix this as well