UBC Algebra and Algebraic Geometry Seminar: Pablo Ocal

Tableaux are fundamental objects in representation theory and combinatorics, and variations of the Schensted algorithm have endowed them with rich algebraic structures. In this talk I will discuss a naive monoid structure on the set of semistandard Young tableaux that does not arise as an insertion algorithm, and the good properties inherited by its associated algebra. We will then mention two applications of our work; one to algebraic geometry, and another to representation theory. For the first, we will show that the tableaux algebra is a flat degeneration of the algebra of global sections of the partial flag variety. For the second, we will show that this naive monoid structure of semistandard Young tableaux induces a crystal embedding when applied to the highest (or lowest) weight vectors.