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<p>Let <i>k</i> be a field of positive characteristic <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p&gt;2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>&gt;</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. Generalizing a result of Farnsteiner and Strade (Math. Z., <b>206</b>, 153–168, 1991), we study the links between coinduced representations and induced representations in the case of restricted Lie superalgebras. As a corollary, we prove a duality property concerning the kernel of coinduced representations of Lie <i>k</i>-superalgebras. This property was already proved by Duflo (Invent. Math., <b>67</b>, 385–393, 1982) for Lie algebras in any characteristic under more restrictive finiteness conditions. It was then generalized to Lie superalgebras in characteristic 0 in previous works Chemla (PhD, 1990; Annales de l’Institut Fourier, <b>44</b>, 1067–1090, 1994 and Mathematische Annalen, <b>297</b>, 371–382, 1994).</p>

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Duality Properties for Induced and Coinduced Representations in Positive Characteristic

  • 期刊论文

  • 发表日期：

    2026年3月11日

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  • Sophie Chemla

摘要

Let k be a field of positive characteristic \(p>2\) p > 2 . Generalizing a result of Farnsteiner and Strade (Math. Z., 206, 153–168, 1991), we study the links between coinduced representations and induced representations in the case of restricted Lie superalgebras. As a corollary, we prove a duality property concerning the kernel of coinduced representations of Lie k-superalgebras. This property was already proved by Duflo (Invent. Math., 67, 385–393, 1982) for Lie algebras in any characteristic under more restrictive finiteness conditions. It was then generalized to Lie superalgebras in characteristic 0 in previous works Chemla (PhD, 1990; Annales de l’Institut Fourier, 44, 1067–1090, 1994 and Mathematische Annalen, 297, 371–382, 1994).