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Bitableaux and Zero Sets of Dual Canonical Basis Elements

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Abstract

We state new results concerning the zero sets of polynomials belonging to the dual canonical basis of \({\mathbb{C}[x_1, 1, . . . , x_n, n]}\) . 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.

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Authors and Affiliations

  1. Department of Mathematics, KAP 108, University of Southern California, 3670 South Vermont Avenue, Los Angeles, CA, 90089-2532, USA

    Brendon Rhoades

  2. Department of Mathematics, Christmas-Saucon Hall, Lehigh University, 14 East Packer Avenue, Bethlehem, PA, 18015, USA

    Mark Skandera

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  1. Brendon Rhoades
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Rhoades, B., Skandera, M. Bitableaux and Zero Sets of Dual Canonical Basis Elements. Ann. Comb. 15, 499–528 (2011). https://doi.org/10.1007/s00026-011-0103-8

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