Double orthodontia formulas and Lascoux positivity

Motivated by our search for a representation theoretic avatar for double Grothendieck polynomials, we extend Magyar’s orthodontia formula for Schubert polynomials. Our formula gives a curious positivity result: Writing $\mathfrak S_w(\mathbf x, \mathbf y)$ for a vexillary double Schubert polynomial, the polynomial $x_1^n \dots x_n^n \mathfrak S_w(x_n^{-1}, \dots, x_1^{-1}; 1, \dots, 1)$ is a graded nonnegative sum of Lascoux polynomials. Joint work with Avery St. Dizier.

For information about the Richard P. Stanley Seminar in Combinatorics, visit https://math.mit.edu/combin/