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Let $\\Phi$ be the root system of $G$, and $\\Phi^+$ be the set of positive roots with respect to $B$.\n  A subset of $\\Phi^+$ is called a rook placement if it consists of roots with pairwise non-positive inner products. To each rook placement $D$ one can associate the coadjoint orbit $\\Omega_D$ of $B$ in $\\nt^*$. By definition, $\\Omega_D$ is the orbit of $f_D$, where $f_D$ is the sum of root covectors corresponging to the roots from $D$. 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Vasyukhin, Mikhail V. Ignatyev","submitted_at":"2013-10-11T15:20:50Z","abstract_excerpt":"Let $G$ be a complex reductive group, $B$ be a Borel subgroup of G, $\\nt$ be the Lie algebra of the unipotent radical of $B$, and $\\nt^*$ be its dual space. Let $\\Phi$ be the root system of $G$, and $\\Phi^+$ be the set of positive roots with respect to $B$.\n  A subset of $\\Phi^+$ is called a rook placement if it consists of roots with pairwise non-positive inner products. To each rook placement $D$ one can associate the coadjoint orbit $\\Omega_D$ of $B$ in $\\nt^*$. By definition, $\\Omega_D$ is the orbit of $f_D$, where $f_D$ is the sum of root covectors corresponging to the roots from $D$. 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