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<p>The Popov–Vinberg variety of a simply connected, split, semisimple algebraic group <i>G</i> is a singular affine variety that contains the basic affine space <i>G</i>/<i>U</i> as a Zariski open subset. It is defined as the spectrum of the ring of functions on <i>G</i>/<i>U</i>, and can also be identified with the universal symplectic implosion for the maximal compact subgroup of <i>G</i>. We provide a recursive procedure for computing the intersection cohomology of this variety, with an emphasis on the case where <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(G = {\text {SL}}_n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mo>=</mo> <msub> <mtext>SL</mtext> <mi>n</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Intersection Cohomology of Popov–Vinberg Varieties

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月3日

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  • Andrew Dancer,
  • Johan Martens,
  • Nicholas Proudfoot

摘要

The Popov–Vinberg variety of a simply connected, split, semisimple algebraic group G is a singular affine variety that contains the basic affine space G/U as a Zariski open subset. It is defined as the spectrum of the ring of functions on G/U, and can also be identified with the universal symplectic implosion for the maximal compact subgroup of G. We provide a recursive procedure for computing the intersection cohomology of this variety, with an emphasis on the case where \(G = {\text {SL}}_n\) G = SL n .