Abstract
By explicitly describing a cellular decomposition we determine the Borel invariant cycles that generate the Chow groups of the quotient of a reductive group by a Levi subgroup. For illustration we consider the variety of polarizations SLn/S(GLp×GLq), and we introduce the notion of a sect for describing its cellular decomposition. In particular, for p=q, we show that the Bruhat order on the sect corresponding to the dense cell is isomorphic, as a poset, to the rook monoid with the Bruhat-Chevalley-Renner order.
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