Characteristic classes of Borel orbits of square-zero upper-triangular matrices

Anna Melnikov provided a parametrization of Borel orbits in the affine variety square-zero n×n matrices by set involutions symmetric group. A related combinatorics leads to construction Bott-Samelson type resolution orbit closures. This allows compute cohomological and K-theoretic invariants orbits: fundamental classes, Chern-Schwartz-MacPherson classes motivic Chern torus-equivariant theories. The formulas are given terms Demazure-Lusztig operations. case upper-triangular is rich enough include information about double Hom(Ck,Cm) for k+m=n. We recall relation with Schubert polynomials show analogous interpretation Rimányi-Tarasov-Varchenko trigonometric weight function.