Faculty of Social Sciences

Algebra- och geometriseminarium: Combinatorial invariance of KLV polynomials for fixed point free involutions

  • Date: 2/13/2018 at 3:15 PM
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Nancy Abdallah (Linköping)
  • Contact person: Volodymyr Mazorchuk
  • Seminarium

Let S_2n be the symmetric group of permutation of {1,..., 2n}, and F_2n in S_2n be the set of fixed points free involutions. To every interval [u,v] in the poset F_2n ordered by the Bruhat order, we associate a KLV-polynomial P_{u,v}. Using a combinatorial concept called Special Partial Matching or SPM, we prove that these polynomials are combinatorially invariant for upper intervals, i.e. for intervals [u, w_0] where w_0 is the maximal element of F_2n . This gives a generalization of the combinatorial invariance of the classical Kazhdan-Lusztig polynomials. This is a joint work with Axel Hultman.