Flag variety bundles encoding pseudo-product structures

This talk will introduce a natural construction for encoding codimension 1 pseudo-product structures into filtered manifolds amenable to analysis by Tanaka prolongation techniques, and its application to local geometry of CR hypersurfaces. Classically, Tanaka prolongation has only been applicable to maximally nondegenerate pseudo-product structures, while our new techniques require much less. The construction recursively produces levels in a tower of fiber bundles inheriting filtered manifold structures from the underlying geometry. In successful cases, it produces an induced filtered structure with finite-dimensional prolongation, bringing the underlying pseudo-product structure equivalence problems into the scope of classical Tanaka prolongation techniques. As a practical demonstration, we will cover the general construction applied to $(2k+3)$-dimensional $k$-nondegenerate CR hypersurfaces, a complete description of the resulting filtered manifolds’ Tanaka symbols, and their algebraic prolongations. The talk is based on joint work with Boris Doubrov and Igor Zelenko.