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Characteristic classes of Borel orbits of square-zero upper-triangular matrices.
- Source :
-
Journal of Algebra . May2022, Vol. 598, p351-384. 34p. - Publication Year :
- 2022
-
Abstract
- Anna Melnikov provided a parametrization of Borel orbits in the affine variety of square-zero n × n matrices by the set of involutions in the symmetric group. A related combinatorics leads to a construction a Bott-Samelson type resolution of the orbit closures. This allows to compute cohomological and K-theoretic invariants of the orbits: fundamental classes, Chern-Schwartz-MacPherson classes and motivic Chern classes in torus-equivariant theories. The formulas are given in terms of Demazure-Lusztig operations. The case of square-zero upper-triangular matrices is rich enough to include information about cohomological and K-theoretic classes of the double Borel orbits in Hom (C k , C m) for k + m = n. We recall the relation with double Schubert polynomials and show analogous interpretation of Rimányi-Tarasov-Varchenko trigonometric weight function. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 598
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 155494325
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2022.01.031