A tightness property of relatively smooth permutations

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It is well known that many geometric properties of Schubert varieties of type A (and others) can be interpreted combinatorially. Given two permutations w, x is an element of S-n we give a combinatorial consequence of the property that the smooth locus of the Schubert variety X-w contains the Schubert cell Y-x. This provides a necessary ingredient for the interpretation of recent representation-theoretic results of the author with Minguez in terms of identities of Kazhdan-Lusztig polynomials. (C) 2018 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)59-84
Number of pages26
JournalJournal Of Combinatorial Theory Series A
StatePublished - Apr 2019

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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