I'm not sure if you've already travelled or not ........
UA do not have a ZED agreement with HA. Quite possibly you may have one with us, in which case it is not bilateral.

If you have paid a Y class fare, you are permitted to travel in Y class. If it's a 3 cabin aircraft, there is a possibility you could be accomodated in Business class.
However, some points to remember :
On paper, you are entitled to your ticketed class
UA onload standby's at the gate and our own employees are boarded strictly by seniority - i.e date of joining. This is followed by Alliance carriers and lastly, all other
interliners.
If seats are full in Y class, according to our agreement and the fare you have paid, you may be told to return another day or if the gate agent is feeling
particularly generous, onload you into a higher class. Since you work for HA, I would guess that it all depends on what experience the gate agent has had
themselves with HA on how you will be accomodated !