FLAG VARIETIES AND THE YANG-BAXTER EQUATION

We investigate certain bases of Hecke algebras defined by means of the Yang-Baxter equation, which we call Yang-Baxter bases. These bases ar e essentially self-adjoint with respect to a canonical bilinear form. In the case of the degenerate Hecke algebra, we identify the coefficie nts in the expansion of the Yang-Baxter basis on the usual basis of th e algebra with specializations of double Schubert polynomials. We also describe the expansions associated to other specializations of the ge neric Hecke algebra.