The $ξ$-stability on the affine grassmannian

Details The $ξ$-stability on the affine grassmannian The $ξ$-stability on the affine grassmannian

2012-02-05

arxiv.org/abs/1202.0987v1

Mathematics

Algebraic Geometry

19 pages, 1 figure

Scientific paper

We introduce a notion of $\xi$-stability on the affine grassmannian $\xx$ for
the classical groups. For the group $\mathrm{SL}_{d}$, we calculate the
Poincar\'e series of the quotient $\xx^{\xi}/T$ of the stable part $\xx^{\xi}$
by the maximal torus $T$ by a process analogue to the Harder-Narasimhan
reduction.

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