Formulas for torus-equivariant fundamental classes of symmetric subgroup orbit closures on the flag variety

Details Formulas for torus-equivariant fundamental classes of symmetric subgroup orbit closures on the flag variety Formulas for torus-equivariant fundamental classes of symmetric subgroup orbit closures on the flag variety

2012-01-20

arxiv.org/abs/1201.4397v1

Mathematics

Algebraic Geometry

Parts of the author's PhD thesis. 87 pages (includes appendix with multiple figures and tables). Comments/questions/correction

Scientific paper

Suppose that $G=SL(n,\C)$, $SO(2n+1,\C)$, $Sp(2n,\C)$, or $SO(2n,\C)$, and let $K$ be any symmetric subgroup of $G$ (i.e., $K = G^{\theta}$ for $\theta$ an involution of $G$). Let $S \subset K$ be a maximal torus. We use equivariant localization to determine formulas for the $S$-equivariant fundamental classes of closed $K$-orbits on the flag variety $G/B$. Taking such formulas as a starting point, we then describe the combinatorics of each orbit set, and indicate how divided difference operators can be used to determine formulas for the $S$-equivariant fundamental classes of all remaining orbit closures.

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