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) |
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Pages (from-to) | 951-969 |
Number of pages | 19 |
Journal | Journal of Algebra |
Volume | 324 |
Issue number | 5 |
DOIs | |
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