Constructing a Gröbner basis of Griffin’s ideal

In his Ph.D. thesis, Sean Griffin introduced a family of ideals and found monomial bases for their quotient rings. These rings simultaneously generalize the Delta Conjecture coinvariant rings of Haglund-Rhoades-Shimozono and the cohomology rings of Springer fibers studied by Tanisaki and Garsia-Procesi. We recursively construct a Gröbner basis of Griffin’s ideals with respect to the graded reverse lexicographical order. Consequently, Griffin’s monomial basis is the standard monomial basis. The coefficients of the polynomials in our Gröbner basis are integers and the leading coefficients are one.