Bitableau bases for Garsia-Haiman modules of hollow type |
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| Authors: | Edward E Allen Gregory S Warrington |
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| Institution: | a Department of Mathematics, Wake Forest University, Winston-Salem, NC, USA
b Statistical Genetics & Bioinformatics, Department of Biostatistical Sciences, Wake Forest University Health Sciences, Winston-Salem, NC, USA |
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| Abstract: | Garsia-Haiman modules CXn,Yn]/Iγ are quotient rings in the variables Xn={x1,x2,…,xn} and Yn={y1,y2,…,yn} that generalize the quotient ring CXn]/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. |
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| Keywords: | Garsia-Haiman modules Bitableau bases Bipermanents Bideterminants |
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