The Return of Noncongruent Equal Protection

Contemporary equal protection doctrine touts the principle of congruence: the notion that equal protection means the same thing whether applied to state or to federal laws. The federalism-tinged equal protection analysis at the heart of Justice Kennedy’s opinion in United States v. Windsor, however, necessarily violates the congruence principle. Commentators and courts—especially those deciding how Windsor’s federalism should affect the ever-growing number of state same-sex marriage cases—have so far failed to account for Windsor’s noncongruent equal protection, much less ask whether noncongruence is generally desirable, and if so, what form it should take. This Article draws answers to those questions from the Supreme Court’s alienage discrimination cases, which offer three distinct models of noncongruence, each of which is reflected in Windsor. The alienage cases show that instead of applying different levels of scrutiny to federal and state laws, a better understanding of noncongruence would allow different levels of government to assert different interests in defending their laws. By reconstructing and evaluating the ways that structure and rights intersect in the alienage cases, this Article considers for the first time what the return of noncongruent equal protection could mean both for cases that follow Windsor and for equal protection doctrine more broadly

Bernstein-Gelfand-Gelfand sequences

This paper is devoted to the study of geometric structures modeled on homogeneous spaces G/P, where G is a real or complex semisimple Lie group and $P\subset G$ is a parabolic subgroup. We use methods from differential geometry and very elementary finite-dimensional representation theory to construct sequences of invariant differential operators for such geometries, both in the smooth and the holomorphic category. For G simple, these sequences specialize on the homogeneous model G/P to the celebrated (generalized) Bernstein-Gelfand-Gelfand resolutions in the holomorphic category, while in the smooth category we get smooth analogs of these resolutions. In the case of geometries locally isomorphic to the homogeneous model, we still get resolutions, whose cohomology is explicitly related to a twisted de Rham cohomology. In the general (curved) case we get distinguished curved analogs of all the invariant differential operators occurring in Bernstein-Gelfand-Gelfand resolutions (and their smooth analogs). On the way to these results, a significant part of the general theory of geometrical structures of the type described above is presented here for the first time.Comment: 45 page