English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Anna Melnikov provided a parametrization of Borel orbits in the affinevariety of square-zero $n \times n$ matrices by the set of involutions in thesymmetric group. A related combinatorics leads to a construction aBott-Samelson type resolution of the orbit closures. This allows to computecohomological and K-theoretic invariants of the orbits: fundamental classes,Chern-Schwartz-MacPherson classes and motivic Chern classes intorus-equivariant theories. The formulas are given in terms of Demazure-Lusztigoperations. The case of square-zero upper-triangular matrices is reach enoughto include information about cohomological and K-theoretic classes of thedouble Borel orbits in $Hom(\mathbb C^k,\mathbb C^m)$ for $k+m=n$. We recallthe relation with double Schubert polynomials and show analogous interpretationof Rim\'anyi-Tarasov-Varchenko trigonometric weight function.

Characteristic classes of Borel orbits of square-zero upper-triangular matrices