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

School of Mathematics

Research output: Contribution to journal › Article › peer-review

16 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: [email protected] (T.K. Petersen), [email protected] (P. Pylyavskyy), [email protected] (D.E. Speyer). 1 Supported by a Research Fellowship from the Clay Mathematics Institute.

Keywords

Gelfand-Tsetlin patterns
Non-crossing tableaux
Standard monomials

Publisher link

10.1016/j.jalgebra.2010.05.001

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title = "A non-crossing standard monomial theory",

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.",

keywords = "Gelfand-Tsetlin patterns, Non-crossing tableaux, Standard monomials",

author = "Petersen, {T. Kyle} and Pavlo Pylyavskyy and Speyer, {David E.}",

note = "Funding Information: E-mail addresses: [email protected] (T.K. Petersen), [email protected] (P. Pylyavskyy), [email protected] (D.E. Speyer). 1 Supported by a Research Fellowship from the Clay Mathematics Institute.",

year = "2010",

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AU - Pylyavskyy, Pavlo

AU - Speyer, David E.

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PY - 2010/9

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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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SP - 951

EP - 969

JO - Journal of Algebra

JF - Journal of Algebra

IS - 5

ER -

A non-crossing standard monomial theory

Abstract

Bibliographical note

Keywords

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