Dear [name of manager or supervisor],
I am writing this letter to request for a new seat assignment as I don’t feel comfortable in my current one. My seat is located next to [Name of colleague], whom I don’t get along with. I think that we can relieve the tension between us if I can be allowed to move to a new seat. I understand if this action may not seem professional to you and that I need to address this issue in some other way. But I feel that things will get even more unprofessional and unproductive if the same seating arrangements remain.
I appreciate your consideration of this request.