We provide explicit formulas for computing the motivic Chern and Hirzebruch classes of degeneracy loci, especially those coming from the symplectic and odd orthogonal Grassmannians. The Chern--Schwartz--MacPherson classes, K-theory classes, and Cappell--Shaneson L-classes arise as specializations of the motivic Chern and Hirzebruch classes. Our result is the analogue of the result of Anderson--Chen--Tarasca for the degeneracy loci from the ordinary Grassmannians. As applications, we obtain the motivic Chern and Hirzebruch classes of orthogonal and symplectic orbit closures in flag varieties.
Categories: math.AG math.CO