Degenerations of kk‐positive surface group representations

We introduce ‐ positive representations , a large class of ‐Anosov surface group representations into that share many features with Hitchin representations, and we study their degenerations: unless they are Hitchin, they can be deformed to non‐discrete representations, but any limit is at least ‐positive and irreducible limits are ‐positive. A major ingredient, of independent interest, is a general limit theorem for positively ratioed representations.