Bitableaux bases for Garsia-Haiman modules of hollow type
Abstract
Garsia-Haiman modules are quotient rings in 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 bitableaux 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.
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