Bitableaux bases for Garsia-Haiman modules of hollow type

2006/10/03 by Edward E. Allen, Allen, Edward E., Miranda E. Cox +3
Mathematics · #05E05 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E05

paper · pdf · doi:10.48550/arxiv.math/0610095

26 pages

arxiv created 2006/10/03 · arxiv updated 2009/12/01

Abstract

Garsia-Haiman modules are quotient rings in variables X_n=x₁, x₂, ..., x_n and Y_n=y₁, y₂, ..., 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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