## View abstract

### Session S10 - Categorification, Higher Representation Theory, and Homological Knot Invariants

Thursday, July 15, 15:20 ~ 15:55 UTC-3

## Uncrowding algorithm for hook-valued tableaux

### Anne Schilling

Whereas set-valued tableaux are the combinatorial objects associated to stable Grothendieck polynomials, hook-valued tableaux are associated to stable canonical Grothendieck polynomials. In this paper, we define a novel uncrowding algorithm for hook-valued tableaux. The algorithm uncrowds'' the entries in the arm of the hooks and yields a set-valued tableau and a column-flagged increasing tableau. We prove that our uncrowding algorithm intertwines with crystal operators. An alternative uncrowding algorithm that uncrowds'' the entries in the leg instead of the arm of the hooks is also given. As an application of uncrowding, we obtain various expansions of the canonical Grothendieck polynomials.