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Abstract <p> We consider two <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1176_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(S\)</EquationSource> </InlineEquation>-dual hyperspherical varieties of the group <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1176_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="81" /> </InlineMediaObject> <EquationSource Format="TEX">\(G_2\times\operatorname{SL}(2)\)</EquationSource> </InlineEquation>: an equivariant slice for <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1176_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(G_2\)</EquationSource> </InlineEquation> and the symplectic representation of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1176_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="67" /> </InlineMediaObject> <EquationSource Format="TEX">\(G_2 \times \operatorname{SL}_2\)</EquationSource> </InlineEquation> in the odd part of the basic classical Lie superalgebra <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1176_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathfrak{g}(3)\)</EquationSource> </InlineEquation>. For these varieties, we check the equality of the numbers of irreducible components of their Lagrangian subvarieties (zero levels of the moment maps of Borel subgroups’ actions), conjectured by M. Finkelberg, V. Ginzburg, and R. Travkin. </p>

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Lagrangian Subvarieties of Hyperspherical Varieties Related to \(G_2\)

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Nikolay Kononenko

摘要

Abstract

We consider two \(S\) -dual hyperspherical varieties of the group \(G_2\times\operatorname{SL}(2)\) : an equivariant slice for \(G_2\) and the symplectic representation of \(G_2 \times \operatorname{SL}_2\) in the odd part of the basic classical Lie superalgebra \(\mathfrak{g}(3)\) . For these varieties, we check the equality of the numbers of irreducible components of their Lagrangian subvarieties (zero levels of the moment maps of Borel subgroups’ actions), conjectured by M. Finkelberg, V. Ginzburg, and R. Travkin.