Stable Branching and Grothendieck Limits for Restricted Lie Algebras of Cartan Type

Let k be an algebraically closed field of characteristic p>3. For the zero-p-character towers of the four restricted Cartan-type families, we determine induction and restriction by a finite intrinsic rule and construct the induction and restriction Grothendieck limits naturally associated with the tower. The principal device is a projective-Hom branching receiver, whose right-hand side is the nullity of an explicit intertwiner matrix. The finite branching matrices assemble into four stable lattices, with an integral duality, a stable Cartan bridge and defect, a branching curvature algebra, and an idempotent-complete exact 2-colimit category. Closed de Rham branching rows are given for the Witt and Special towers. This answers Problem 2 of Benkart and Feldvoss.