Sorry for the delay! It's fairly simple.
1. You have a column on your objects you want secured as an LTREE[] 2. You add a GIST index on that column
The values should be the different hierarchy paths to access the object starting with a "type" e.g departments.root.deptA
When you run a query, depending on how you want to access you use a <@ query. E.g. I'm a user with root access to all depts "col <@ 'departments.root'::ltree" or I'm a user in dept A "col <@ 'departments.root.deptA'::ltree" etc
The values should be the different hierarchy paths to access the object starting with a "type" e.g departments.root.deptA
When you run a query, depending on how you want to access you use a <@ query. E.g. I'm a user with root access to all depts "col <@ 'departments.root'::ltree" or I'm a user in dept A "col <@ 'departments.root.deptA'::ltree" etc