Soergel Bimodules and the Shape of Bruhat Intervals

  title={Soergel Bimodules and the Shape of Bruhat Intervals},
  author={George Melvin and William Slofstra},
Given an element w of a Coxeter group, let ai(w) be the number of elements less than w in Bruhat order. A theorem of Björner and Ekedahl states that if W is crystallographic, then ai(w) ≤ aj(w) for all 0 ≤ i < j ≤ `(w) − i. Their proof uses the hard Lefschetz property in intersection cohomology. In this note we extend Björner and Ekedahl’s theorem to all… CONTINUE READING