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.
Bibliographical noteFunding Information:
E-mail addresses: firstname.lastname@example.org (T.K. Petersen), email@example.com (P. Pylyavskyy), firstname.lastname@example.org (D.E. Speyer). 1 Supported by a Research Fellowship from the Clay Mathematics Institute.
- Gelfand-Tsetlin patterns
- Non-crossing tableaux
- Standard monomials