A filtration on the cohomology rings of regular nilpotent Hessenberg varieties

Let n be a positive integer. The main result of this manuscript is a construction of a filtration on the cohomology ring of a regular nilpotent Hessenberg variety in GL(n,C)/B$$GL(n,{\mathbb {C}})/B$$ such that its associated graded ring has graded pieces (i.e., homogeneous components) isomorphic to rings which are related to the cohomology rings of Hessenberg varieties in GL(n-1,C)/B$$GL(n-1,{\mathbb {C}})/B$$, showing the inductive nature of …