The torus equivariant cohomology rings of Springer varieties
| Autor: | Tatsuya Horiguchi, Hiraku Abe |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Ring (mathematics)
Pure mathematics 010102 general mathematics Torus 0102 computer and information sciences Mathematics::Algebraic Topology 01 natural sciences Mathematics::K-Theory and Homology 010201 computation theory & mathematics Symmetric group Nilpotent operator FOS: Mathematics Algebraic Topology (math.AT) Equivariant cohomology Equivariant map Mathematics - Algebraic Topology Geometry and Topology Ideal (ring theory) 0101 mathematics Variety (universal algebra) Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Topology and its Applications. 208:143-159 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2016.05.004 |
| Popis: | The Springer variety of type $A$ associated to a nilpotent operator on $\mathbb{C}^n$ in Jordan canonical form admits a natural action of the $\ell$-dimensional torus $T^{\ell}$ where $\ell$ is the number of the Jordan blocks. We give a presentation of the $T^{\ell}$-equivariant cohomology ring of the Springer variety through an explicit construction of an action of the $n$-th symmetric group on the $T^{\ell}$-equivariant cohomology group. The $T^{\ell}$-equivariant analogue of so called Tanisaki's ideal will appear in the presentation. Comment: 14 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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