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    Mathematics, Northeastern University, Boston

    A Deodhar-type stratification on the double flag variety

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    We describe a stratification on the double flag variety G/B +times G/B - of a complex semisimple algebraic group G analogous to the Deodhar stratification on the flag variety G/B +, which is a refinement of the stratification into orbits both for B +times B - and for the diagonal action of G, just as Deodhar's stratification refines the orbits of B + and B -. We give a coordinate system on each stratum, and show that all strata are coisotropic subvarieties. Also, we discuss possible connections to the positive and cluster geometry of G/B +times G/B -, which would generalize results of Fomin and Zelevinsky on double Bruhat cells and Marsh and Rietsch on double Schubert cells.

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    Description

    Title : A Deodhar-type stratification on the double flag variety
    Author(s) : Ben Webster, Milen Yakimov
    Abstract : We describe a stratification on the double flag variety G/B +times G/B - of a complex semisimple algebraic group G analogous to the Deodhar stratification on the flag variety G/B +, which is a refinement of the stratification into orbits both for B +times B - and for the diagonal action of G, just as Deodhar's stratification refines the orbits of B + and B -. We give a coordinate system on each stratum, and show that all strata are coisotropic subvarieties. Also, we discuss possible connections to the positive and cluster geometry of G/B +times G/B -, which would generalize results of Fomin and Zelevinsky on double Bruhat cells and Marsh and Rietsch on double Schubert cells.
    Keywords : algebraic geometry, symplectic geometry

    Subject : unspecified
    Area : Other
    Language : English
    Year : 2006

    Affiliations Mathematics, Northeastern University, Boston
    Journal : Transformation Groups
    Volume : 12
    Issue : 4
    Pages : 769 - 785
    Url : http://www.springerlink.com/index/10.1007/s00031-007-0061-8
    Doi : 10.1007/s00031-007-0061-8

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