A non-crossing standard monomial theory

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

doi:10.1016/j.jalgebra.2010.05.001

A non-crossing standard monomial theory

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

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	951-969
Number of pages	19
Journal	Journal of Algebra
Volume	324
Issue number	5
DOIs	https://doi.org/10.1016/j.jalgebra.2010.05.001
State	Published - 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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10.1016/j.jalgebra.2010.05.001

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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.",

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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.",

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AU - Petersen, T. Kyle

AU - Pylyavskyy, Pavlo

AU - Speyer, David E.

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N2 - 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.

AB - 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.

KW - Gelfand-Tsetlin patterns

KW - Non-crossing tableaux

KW - Standard monomials

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