# Pureté des fibres de Springer affines pour GL_4

Abstract : This thesis consists of two parts. In the first part, we prove the purity of affine Springer fibers for $\gl_{4}$ in the unramified case. More precisely, we have constructed a family of non standard affine pavings for the affine grassmannian, which induce an affine paving for the affine Springer fiber. In the second part, we introduce a notion of $\xi$-stability on the affine grassmannian $\xx$ for the group $G=\gl_{d}$, and we calculate the Poincaré polynomial of the quotient $\xx^{\xi}/T$ of the stable part $\xxs$ by the maximal torus $T$ by a process analogue to the Harder-Narasimhan reduction.
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### Citation

Zongbin Chen. Pureté des fibres de Springer affines pour GL_4. Mathématiques générales [math.GM]. Université Paris Sud - Paris XI, 2011. Français. ⟨NNT : 2011PA112266⟩. ⟨tel-00656163⟩

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