The Deodhar stratification via hybrid normal forms
by
Endenicher Allee 60/1-016 - Lipschitzsaal
Mathezentrum
The intersections of positive and negative Schubert cells play an important role in Kazhdan-Lusztig theory as they geometrize the R-polynomials. Today, these varieties are known as Kazhdan-Lusztig-Deodhar-Richardson (or short KLDR) varieties. In the '80s, Deodhar introduced a decomposition of KLDR varieties of any flag varieties with the remarkable property that each component is isomorphic to a product of an affine space and a torus. In a recent work on standard extension algebras, Eberhardt and Stroppel introduced a further decomposition of the KLDR varieties of Grassmannians to which they referred to as Bruhat-type stratification. The components of this decomposition are again of the same shape as the components of the Deodhar decomposition. In this talk, we will see that the Deodhar and Bruhat-type decomposition actually coincide.
flake@math.uni-bonn.de