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<p>In this article we describe the general and special projectivity groups for all irreducible residues of all thick, irreducible, spherical buildings of type <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( \mathsf {B_{n}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="sans-serif">B</mi> <mi mathvariant="sans-serif">n</mi> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( \mathsf {C_{n}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="sans-serif">C</mi> <mi mathvariant="sans-serif">n</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathsf {F_4}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="sans-serif">F</mi> <mn mathvariant="sans-serif">4</mn> </msub> </math></EquationSource> </InlineEquation>, and rank at least 3. This determines the exact structure and action of Levi subgroups of parabolic subgroups of groups of Lie type related to those buildings.</p>

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Groups of projectivities in spherical buildings of non-simply laced type

  • 期刊论文

  • 发表日期：

    2026年4月9日

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  • Sira Busch,
  • Hendrik Van Maldeghem

摘要

In this article we describe the general and special projectivity groups for all irreducible residues of all thick, irreducible, spherical buildings of type \( \mathsf {B_{n}}\) B n , \( \mathsf {C_{n}}\) C n and \(\mathsf {F_4}\) F 4 , and rank at least 3. This determines the exact structure and action of Levi subgroups of parabolic subgroups of groups of Lie type related to those buildings.