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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb{F}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="double-struck">F</mi> </mrow> </math></EquationSource> </InlineEquation> be an algebraically closed field of odd prime characteristic <i>p</i>. Using only transfers and norms, we describe a separating set for each indecomposable modular representation of the dihedral groups <i>D</i><sub>2<i>p</i></sub> over the field <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb{F}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="double-struck">F</mi> </mrow> </math></EquationSource> </InlineEquation>. Our construction is recursive and the size of every separating set depends only on the dimension of the representation.</p>

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Modular separating invariants for the dihedral groups D2p

  • 期刊论文

  • 发表日期：

    2025年11月26日

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  • Panpan Jia,
  • Jizhu Nan,
  • Yongsheng Ma

摘要

Let \(\mathbb{F}\) F be an algebraically closed field of odd prime characteristic p. Using only transfers and norms, we describe a separating set for each indecomposable modular representation of the dihedral groups D2p over the field \(\mathbb{F}\) F . Our construction is recursive and the size of every separating set depends only on the dimension of the representation.