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<p>Describing the decomposition of the Foulkes module <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(F_b^a\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>F</mi> <mi>b</mi> <mi>a</mi> </msubsup> </math></EquationSource> </InlineEquation> into irreducible Specht modules is an open problem when both <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(a,b &gt; 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>&gt;</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. In this article we provide a new approach for the Generalized Foulkes module <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(F_{\nu }^a\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>F</mi> <mrow> <mi>ν</mi> </mrow> <mi>a</mi> </msubsup> </math></EquationSource> </InlineEquation> (with arbitrary partition <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\nu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ν</mi> </math></EquationSource> </InlineEquation> of <i>b</i>) through its restriction to a maximal Young subgroup <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({S_b \times S_{ab -b}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>S</mi> <mi>b</mi> </msub> <mo>×</mo> <msub> <mi>S</mi> <mrow> <mi>a</mi> <mi>b</mi> <mo>-</mo> <mi>b</mi> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Some Properties of the Generalized Foulkes Module

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月12日

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  • Pál Hegedüs,
  • Sai Praveen Madireddi

摘要

Describing the decomposition of the Foulkes module \(F_b^a\) F b a into irreducible Specht modules is an open problem when both \(a,b > 3\) a , b > 3 . In this article we provide a new approach for the Generalized Foulkes module \(F_{\nu }^a\) F ν a (with arbitrary partition \(\nu \) ν of b) through its restriction to a maximal Young subgroup \({S_b \times S_{ab -b}}\) S b × S a b - b .