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We obtain a criterion for rational smoothness of an algebraic variety with a torus action, with applications to orbit closures in flag varieties, and to closures of double classes in regular group completions.
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A Deodhar-type stratification on the double flag variety
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We describe a partition of the double flag variety G/B+ × G/B- of a complex semisimple algebraic group G analogous to the Deodhar partition on the flag variety G/B+.
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Also, we discuss possible connections to the positive and cluster geometry of G/B+ × 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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Hardy Spaces on the Plane and Double Fourier Transforms
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