The $$\xi $$ ξ -stability on the affine grassmannian
| Autor: | Zongbin Chen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Classical group
Pure mathematics Group (mathematics) General Mathematics Mathematical analysis Vector bundle Affine Grassmannian (manifold) Moduli space Condensed Matter::Materials Science Mathematics::Algebraic Geometry Maximal torus Algebraic curve Mathematics::Symplectic Geometry Quotient Mathematics |
| Popis: | We introduce a notion of $$\xi $$ ξ -stability on the affine grassmannian $${\fancyscript{X}}$$ X for the classical groups, this is the local version of the $$\xi $$ ξ -stability on the moduli space of Higgs bundles on a curve introduced by Chaudouard and Laumon. We prove that the quotient $${\fancyscript{X}}^{\xi }/T$$ X ξ / T of the stable part $${\fancyscript{X}}^{\xi }$$ X ξ by the maximal torus $$T$$ T exists as an ind- $$k$$ k -scheme, and we introduce a reduction process analogous to the Harder-Narasimhan reduction for vector bundles over an algebraic curve. For the group $${\mathrm {SL}}_{d}$$ SL d , we calculate the Poincaré series of the quotient $${\fancyscript{X}}^{\xi }/T$$ X ξ / T . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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