Minimum requirements to get a jersey retired:
— First team All-American
— Recipient of major national award
— University graduate
— Minimum 15-year waiting period
— Significant accomplishments after BYU graduation (athletics, community, church)
— Faithful member of LDS Church or other religious affiliation

Not sure if all of these are still requirements. The criteria came from an article about Ainge's jersey retirement: https://byucougars.com/news/2003/02/18/byu-to-retire-danny-ainge-jersey-at-byu-csu-game