Extends Lusztig total positivity to symmetric spaces G/K via Hausdorff closure, proves cell decomposition with positive parametrizations and subtraction-free transitions.
Closure relations for totally nonnegative cells in G/P
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abstract
The totally nonnegative part of a partial flag variety G/P is known to have a decomposition into semi-algebraic cells. We show that the closure of a cell is again a union of cells and give a combinatorial description of the closure relations. The totally nonnegative cells are defined by intersecting the totally nonnegative part with a certain stratification of G/P defined by Lusztig. We also verify the same closure relations for these strata.
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Total positivity and symmetric spaces
Extends Lusztig total positivity to symmetric spaces G/K via Hausdorff closure, proves cell decomposition with positive parametrizations and subtraction-free transitions.