The finite minuscule and d-complete posets generalize Young and shifted Young diagrams.  They have many nice combinatorial properties; for example, minuscule posets are Gaussian and Sperner, and d-complete posets have the hook length and jeu de taquin properties.  Infinite analogs of the colored minuscule posets were used by R.M. Green to construct representations of many…

Multiline queues were introduced by Ferrari and Matrin as a tool for understanding the steady state of the Totally Asymmetric Simple Exclusion Process (TASEP) on a ring. Since then, they have attracted independent interest as combinatorial objects. A queue can be described as a transformation of words by a combinatorial rule (related to the Lascoux-Schützenberger action of the symmetric group). A…

A Kirillov-Reshetikhin(KR) module is a certain finite dimensional U_q'(\mathfrak{g}) module that is determined by its Drinfeld polynomials. KR modules are an important class of modules for quantum groups with many applications to Mathematical physics. KR modules are conjectured to have many nice properties, one of which is the existence of a crystal basis. In this talk, we will give a…