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• W2922335905 abstract "In this paper we construct and prove superintegrability of spin Calogero-Moser type systems on symplectic leaves of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper K 1 minus upper T Superscript asterisk Baseline upper G slash upper K 2> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>K</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mi class=MJX-variant mathvariant=normal>∖<!-- ∖ --></mml:mi> <mml:msup> <mml:mi>T</mml:mi> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:mi>G</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>K</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>K_1backslash T^*G/K_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper K 1 comma upper K 2 subset-of upper G> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>K</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mtext> </mml:mtext> <mml:msub> <mml:mi>K</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:mi>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>K_1,space K_2subset G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are subgroups. We call them two-sided spin Calogero-Moser systems. One important type of such systems correspond to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper K 1 equals upper K 2 equals upper K> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>K</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>K</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>K</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>K_1=K_2=K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper K> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=application/x-tex>K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a subgroup of fixed points of Chevalley involution <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=theta colon upper G right-arrow upper G> <mml:semantics> <mml:mrow> <mml:mi>θ<!-- θ --></mml:mi> <mml:mo>:</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mi>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>theta : Gto G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The other important series of examples come from pair <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G subset-of upper G times upper G> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:mi>G</mml:mi> <mml:mo>×<!-- × --></mml:mo> <mml:mi>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>Gsubset Gtimes G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with the diagonal embedding. We explicitly describe examples of such systems corresponding to symplectic leaves of rank one when <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G equals upper S upper L Subscript n> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>=</mml:mo> <mml:mi>S</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>G=SL_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
• W2922335905 created "2019-03-22" @default.
• W2922335905 creator A5011211902 @default.
• W2922335905 date "2021-01-01" @default.
• W2922335905 modified "2023-10-18" @default.
• W2922335905 title "Spin Calogero-Moser models on symmetric spaces" @default.
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• W2922335905 doi "https://doi.org/10.1090/pspum/103.1/01840" @default.
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