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<p>If <i>G</i> is <i>p</i>-solvable, we prove that there exists a McKay bijection that respects the decomposition numbers <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2171_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(d_{\chi \varphi }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>d</mi> <mrow> <mi>χ</mi> <mi>φ</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>, whenever <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2171_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation> is linear.</p>

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McKay bijections and decomposition numbers

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • David Cabrera-Berenguer

摘要

If G is p-solvable, we prove that there exists a McKay bijection that respects the decomposition numbers \(d_{\chi \varphi }\) d χ φ , whenever \(\varphi \) φ is linear.