Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Monday 4
Combinatorics
Karen Yeats
› 17:30 - 19:00 (1h30)
› SFU Harbour Center - Segal Centre Conference Rooms 1400 - 1410
Order Filter Model for Minuscule Plu ̈cker Relations
David C Lax  1  
1 : Dept of Math, The University of North Carolina at Chapel Hill

The Plu ̈cker relations which define the Grassmann manifolds as projective varieties are well known. Grass- mann manifolds are examples of minuscule flag manifolds. We study the generalized Plu ̈cker relations for minuscule flag manifolds independent of Lie type. To do this we combinatorially model the Plu ̈cker coordinates based on Wild- berger's construction of minuscule Lie algebra representations; it uses the colored partially ordered sets known as minuscule posets. We obtain, uniformly across Lie type, descriptions of the Plu ̈cker relations of “extreme weight”. We show that these are “supported” by “double-tailed diamond” sublattices of minuscule lattices. From this, we obtain a complete set of Plu ̈cker relations for the exceptional minuscule flag manifolds. These Plu ̈cker relations are straightening laws for their coordinate rings. 



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