A noncommutative geometric LR rule

Edward Richmond (1) , Vasu Tewari (2) , Stephanie van Willigenburg (3)

1 OSU - Oklahoma State University [Stillwater]
2 University of Washington [Seattle]
3 University of British Columbia - UBC [Vancouver, BC, Canada]

The geometric Littlewood-Richardson (LR) rule is a combinatorial algorithm for computing LR coefficients derived from degenerating the Richardson variety into a union of Schubert varieties in the Grassmannian. Such rules were first given by Vakil and later generalized by Coskun. In this paper we give a noncommutative version of the geometric LR rule. As a consequence, we establish a geometric explanation for the positivity of noncommutative LR coefficients in certain cases.

Mots clés: Combinatorics

Domaines: Combinatoire [math.CO]

Edward Richmond, Vasu Tewari, Stephanie van Willigenburg. A noncommutative geometric LR rule. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6367⟩. ⟨hal-02166336⟩