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Bitableaux bases for Garsia-Haiman modules of hollow type

Edward E. Allen·Miranda E. Cox·Gregory S. Warrington
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Abstract

Garsia-Haiman modules are quotient rings in variables X_n={x_1, x_2, ..., x_n} and Y_n=y_1, y_2, ..., y_n} that generalize the quotient ring C[X_n]/I, where I is the ideal generated by the elementary symmetric polynomials e_j(X_n) 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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Edward E. Allen, Miranda E. Cox, Gregory S. Warrington. 2006-10-03. Bitableaux bases for Garsia-Haiman modules of hollow type. https://arxiv.org/abs/math/0610095

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