Diagrams and Essential Sets for Signed Permutations

  • David Anderson The Ohio State University
Keywords: Essential set, Rank condition, Signed permutation, Schubert variety


We introduce diagrams and essential sets for signed permutations, extending the analogous notions for ordinary permutations.  In particular, we show that the essential set provides a minimal list of rank conditions defining the Schubert variety or degeneracy locus corresponding to a signed permutation.  Our essential set is in bijection with the poset-theoretic version defined by Reiner, Woo, and Yong, and thus gives an explicit, diagrammatic method for computing the latter.
Article Number