We can use the below query for finding the all the responsibility for a particular user.

SELECT fu.user_name,
         fr.responsibility_name,
         furg.start_date,
         furg.end_date
    FROM fnd_user_resp_groups_direct furg,
         fnd_user fu,
         fnd_responsibility_tl fr
   WHERE     fu.user_name = '&user_name'
         AND furg.user_id = fu.user_id
         AND furg.responsibility_id = fr.responsibility_id
         AND fr.language = USERENV ('LANG')
ORDER BY start_date;


We can modify the above query to find all the User associated with a particular responsibility too.

SELECT fu.user_name,
         fr.responsibility_name,
         furg.start_date,
         furg.end_date
    FROM fnd_user_resp_groups_direct furg,
         fnd_user fu,
         fnd_responsibility_tl fr
   WHERE      fr.responsibility_name = '&responsibilty_name'
         AND furg.user_id = fu.user_id
         AND furg.responsibility_id = fr.responsibility_id
         AND fr.language = USERENV ('LANG')
ORDER BY start_date;