Principal specializations of Schubert polynomials in classical types (Q5925603)

There is a remarkable formula for the principal specialization of a type A Schubert polynomial as a weighted sum over reduced words. Taking appropriate limits transforms this to an identity for the backstable Schubert polynomials recently introduced by \textit{T. Lam} et al. [Compos. Math. 157, No. 5, 883--962 (2021; Zbl 07358686)]. In this paper, the authors identify some apparently new analogues of Macdonald's identity for the principal specializations of Schubert polynomials in other classical types B, C, and D and also derive some more general identities for Grothendieck polynomials. The methods used are based on the algebraic techniques of \textit{S. Fomin} and \textit{R. P. Stanley} [Adv. Math. 103, No. 2, 196--207 (1994; Zbl 0809.05091)].