The glue between Young tableaux
Allen Knutson (Berkeley)
Semistandard Young tableaux have been studied for a century in
combinatorics, representation theory, and the algebraic geometry of
determinantal varieties. I'll show how Anders Buch's generalization,
"set-valued tableaux", serve as a sort of glue between ordinary
tableaux, in that all tableaux fit into a simplicial complex with Buch's
tableaux corresponding to lower-dimensional faces. The evidence that this
is a combinatorially natural thing to do is that the simplicial complex is
homeomorphic to a ball.
In fact some Gröbner bases of determinantal varieties handed us this combinatorial structure. I'll give a hint of that connection if time permits.
This work is joint with Ezra Miller (University of Minnesota) and Alex Yong (University of Illinois at Urbana-Champaign).