A Study of the Representations Supported by the Orbit Closure of the Determinant

We show the existence of a large family of representations supported by the orbit closure of the determinant. However, the validity of our result is based on the validity of the celebrated 'Latin Square Conjecture' due to Alon-Tarsi or more precisely on the validity of an equivalent 'Column Latin Square Conjecture' due to Huang-Rota.