To every infinite lower Hessenberg matrix D is associated a linear operator on l2. In this paper we prove the similarity of the operator D − ∆, where ∆ belongs to a certain class of compact operators, to the operator D−∆′, where ∆′ is of rank one. We first consider the case when ∆ is lower triangular and has finite rank; then we extend this to ∆ of infinite rank assuming that D is bounded. In S...

The Springer variety is the set of flags stabilized by a nilpotent operator. In 1976, T.A. Springer observed that this variety’s cohomology ring carries a symmetric group action, and he offered a deep geometric construction of this action. Sixteen years later, Garsia and Procesi made Springer’s work more transparent and accessible by presenting the cohomology ring as a graded quotient of a poly...