A non-crossing standard monomial theory

T. Kyle Petersen, Pavlo Pylyavskyy, David E. Speyer

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

The second author has introduced non-crossing tableaux, objects whose non-nesting analogues are semi-standard Young tableaux. We relate non-crossing tableaux to Gelfand-Tsetlin patterns and develop the non-crossing analogue of standard monomial theory. Leclerc and Zelevinsky's weakly separated sets are special cases of non-crossing tableaux, and we suggest that non-crossing tableaux may help illuminate the theory of weakly separated sets.

Original languageEnglish (US)
Pages (from-to)951-969
Number of pages19
JournalJournal of Algebra
Volume324
Issue number5
DOIs
StatePublished - Sep 2010

Bibliographical note

Funding Information:
E-mail addresses: tkpeters@umich.edu (T.K. Petersen), pylyavskyy@gmail.com (P. Pylyavskyy), speyer@math.mit.edu (D.E. Speyer). 1 Supported by a Research Fellowship from the Clay Mathematics Institute.

Keywords

  • Gelfand-Tsetlin patterns
  • Non-crossing tableaux
  • Standard monomials

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