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• W3208343608 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a reductive algebraic group and let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper Z> <mml:semantics> <mml:mi>Z</mml:mi> <mml:annotation encoding=application/x-tex>Z</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the stabilizer of a nilpotent element <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=e> <mml:semantics> <mml:mi>e</mml:mi> <mml:annotation encoding=application/x-tex>e</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the Lie algebra of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We consider the action of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper Z> <mml:semantics> <mml:mi>Z</mml:mi> <mml:annotation encoding=application/x-tex>Z</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on the flag variety of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and we focus on the case where this action has a finite number of orbits (i.e., <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper Z> <mml:semantics> <mml:mi>Z</mml:mi> <mml:annotation encoding=application/x-tex>Z</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a spherical subgroup). This holds for instance if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=e> <mml:semantics> <mml:mi>e</mml:mi> <mml:annotation encoding=application/x-tex>e</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has height <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=2> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding=application/x-tex>2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In this case we give a parametrization of the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper Z> <mml:semantics> <mml:mi>Z</mml:mi> <mml:annotation encoding=application/x-tex>Z</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-orbits and we show that each <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper Z> <mml:semantics> <mml:mi>Z</mml:mi> <mml:annotation encoding=application/x-tex>Z</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-orbit has a structure of algebraic affine bundle. In particular, in type <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we deduce that each orbit has a natural cell decomposition. In the aim to study the (strong) Bruhat order of the orbits, we define an abstract partial order on certain quotients associated to a Coxeter system. In type <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we show that the Bruhat order of the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper Z> <mml:semantics> <mml:mi>Z</mml:mi> <mml:annotation encoding=application/x-tex>Z</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-orbits can be described in this way." @default.
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• W3208343608 date "2021-10-21" @default.
• W3208343608 modified "2023-09-25" @default.
• W3208343608 title "Parametrization, structure and Bruhat order of certain spherical quotients" @default.
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