Bitableau bases for Garsia–Haiman modules of hollow type

Garsia–Haiman modules C[Xn,Yn]/Iγ are quotient rings in the variables Xn={x1,x2,…,xn} and Yn={y1,y2,…,yn} that generalize the quotient ring C[Xn]/I, where I is the ideal generated by the elementary symmetric polynomials ej(Xn) for 1⩽j⩽n. A bitableau basis for the Garsia–Haiman modules of hollow type is constructed. Applications of this basis to representation theory and other related polynomial spaces are considered.