The cohomology ring of weight varieties and polygon spaces

2002/01/15 by R. F. Goldin
Mathematics · #math.SG #math.AG #math.CO #msc:53D20 #msc:14M15 #msc:05E99

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published as Advances in Mathematics 160 (2001), no. 2, pp. 175-204 · 31 pages, 1 figure

arxiv created 2002/01/15 · arxiv updated 2009/11/30

Abstract

We use a theorem of Tolman and Weitsman to find explicit formulæfor the rational cohomology rings of the symplectic reduction of flag varieties in Cⁿ, or generic coadjoint orbits of SU(n), by (maximal) torus actions. We also calculate the cohomology ring of the moduli space of n points in CP^k, which is isomorphic to the Grassmannian of k-planes in Cⁿ, by realizing it as a degenerate coadjoint orbit.

Related

• Cohomology of symplectic reductions of generic coadjoint orbits
• The cohomology ring of polygon spaces
• The Duistermaat-Heckman formula and the cohomology of moduli spaces of\n polygons
• The cohomology rings of abelian symplectic quotients
• Cohomology rings of character varieties