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Bitableaux and Zero Sets of Dual Canonical Basis Elements
Brendon Rhoades1 and Mark Skandera2
1Department of Mathematics, KAP 108, University of Southern California, 3670 South Vermont Avenue, Los Angeles, CA 90089-2532, USA
2Department of Mathematics, Christmas-Saucon Hall, Lehigh University, 14 East Packer Avenue, Bethlehem, PA 18015, USA
Annals of Combinatorics 15 (3) pp.499-528 July, 2011
AMS Subject Classification: 05E10, 15A15
We state new results concerning the zero sets of polynomials belonging to the dual canonical basis of C[x1,1, . . . , xn,n]. As an application, we show that this basis is related by a unitriangular transition matrix to the simpler bitableau basis popularized by Désarménien- Kung-Rota. It follows that spaces spanned by certain subsets of the dual canonical basis can be characterized in terms of products of matrix minors, or in terms of their common zero sets.
Keywords: dual canonical basis, zero set, bitableau


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