Schur times Schubert via the Fomin-Kirillov algebra

Subalgebras of the Fomin–Kirillov algebra

“…The Fomin-Kirillov algebra E n [7] is a certain noncommutative algebra with generators x ij for 1 ≤ i < j ≤ n that satisfy a simple set of quadratic relations. While it was originally introduced as a tool to study the structure constants for Schubert polynomials, since then the Fomin-Kirillov algebra and its generalizations have received much attention from the perspectives of both combinatorics and algebra: see, for instance, [3,8,13,14,15,16,18,20,21,23,26]. But despite its simple presentation, even some basic questions about E n have eluded an answer thus far, such as whether or not it is finite-dimensional for n ≥ 6.…”

On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials

“…Partial results concerning these problems have been obtained as far as we aware in [45,70,72,73,104,117].…”