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arXiv · 1202.0987

The $\xi$-stability on the affine grassmannian

Zongbin Chen
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Abstract

We introduce a notion of $\xi$-stability on the affine grassmannian $\xx$ for the classical groups, this is the local version of the $\xi$-stability on the moduli space of Higgs bundles on a curve introduced by Chaudouard and Laumon. We prove that the quotient $\xx^{\xi}/T$ of the stable part $\xx^{\xi}$ by the maximal torus $T$ exists as an ind-$k$-scheme, and we introduce a reduction process analogous to the Harder-Narasimhan reduction for vector bundles. For the group $\mathrm{SL}_{d}$, we calculate the Poincar\'e series of the quotient $\xx^{\xi}/T$.

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Zongbin Chen. 2012-02-05. The $\xi$-stability on the affine grassmannian. https://arxiv.org/abs/1202.0987

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