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Medientyp: E-Artikel Titel: The Bruhat order on abelian ideals of Borel subalgebras Beteiligte: Gandini, Jacopo; Maffei, Andrea; Möseneder Frajria, Pierluigi; Papi, Paolo Erschienen: American Mathematical Society (AMS), 2020 Erschienen in: Transactions of the American Mathematical Society Sprache: Englisch DOI: 10.1090/tran/8092 ISSN: 0002-9947; 1088-6850 Schlagwörter: Applied Mathematics ; General Mathematics Entstehung: Anmerkungen: Beschreibung: <p>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 quasi-simple algebraic group over an algebraically closed field <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sans-serif k"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="sans-serif">k</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathsf {k}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> whose characteristic is not very bad for <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 let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper B"> <mml:semantics> <mml:mi>B</mml:mi> <mml:annotation encoding="application/x-tex">B</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a Borel subgroup 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> with Lie algebra <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German b"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">b</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {b}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Given a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper B"> <mml:semantics> <mml:mi>B</mml:mi> <mml:annotation encoding="application/x-tex">B</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-stable abelian subalgebra <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German a"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">a</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {a}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the nilradical of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German b"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">b</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {b}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we parametrize the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper B"> <mml:semantics> <mml:mi>B</mml:mi> <mml:annotation encoding="application/x-tex">B</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-orbits in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German a"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">a</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {a}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and we describe their closure relations.</p>