Characteristic classes of Borel orbits of square-zero upper-triangular matrices
| Autor: | Piotr Rudnicki, Andrzej Weber |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Algebraic Geometry
Algebra and Number Theory Mathematics::K-Theory and Homology FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology Representation Theory (math.RT) Mathematics::Algebraic Topology Algebraic Geometry (math.AG) Mathematics - Representation Theory |
| DOI: | 10.48550/arxiv.2108.03598 |
| Popis: | Anna Melnikov provided a parametrization of Borel orbits in the affine variety of square-zero $n \times n$ 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 reach enough to include information about cohomological and K-theoretic classes of the double Borel orbits in $Hom(\mathbb C^k,\mathbb C^m)$ for $k+m=n$. We recall the relation with double Schubert polynomials and show analogous interpretation of Rim\'anyi-Tarasov-Varchenko trigonometric weight function. Comment: 29 pages |
| Databáze: | OpenAIRE |
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