A non-crossing standard monomial theory

Details A non-crossing standard monomial theory A non-crossing standard monomial theory

2008-06-11

arxiv.org/abs/0806.1776v1

Mathematics

Combinatorics

23 pages, 7 figures

Scientific paper

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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