A characterization of a class of hyperplanes of

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• 作者：Bart De Bruyn ^{bdb@cage.ugent.be" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Symplectic dual polar space ; Hyperplane (of subspace-type) ; Spin-embedding
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：6 January 2017
• 年：2017
• 卷：340
• 期：1
• 页码：3176-3182
• 全文大小：421 K

文摘

A hyperplane of the symplectic dual polar space hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si1.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=90f9da144bfc69630b38688876bc4c52" title="Click to view the MathML source">DW(2n−1,F)hContainer hidden">hCode">h id="mml2" overflow="scroll" altimg="si1.gif">DWw>(2n−1,hvariant="double-struck">F)w>h>, hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si3.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=7ab241b0dfb64c5126c19aefad6c7526" title="Click to view the MathML source">n≥2hContainer hidden">hCode">h id="mml3" overflow="scroll" altimg="si3.gif">n≥2h>, is said to be of subspace-type if it consists of all maximal singular subspaces of hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si4.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=d06018fb790215b959961e90c2b1b1ef" title="Click to view the MathML source">W(2n−1,F)hContainer hidden">hCode">h id="mml4" overflow="scroll" altimg="si4.gif">Ww>(2n−1,hvariant="double-struck">F)w>h> meeting a given hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si5.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=f6ee4a1092228dcac3addc9ef4246976" title="Click to view the MathML source">(n−1)hContainer hidden">hCode">h id="mml5" overflow="scroll" altimg="si5.gif">w>(n−1)w>h>-dimensional subspace of hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si6.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=7b793208a490b4329a368ef0c4d7ab16" title="Click to view the MathML source">PG(2n−1,F)hContainer hidden">hCode">h id="mml6" overflow="scroll" altimg="si6.gif">PGw>(2n−1,hvariant="double-struck">F)w>h>. We show that a hyperplane of hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si1.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=90f9da144bfc69630b38688876bc4c52" title="Click to view the MathML source">DW(2n−1,F)hContainer hidden">hCode">h id="mml7" overflow="scroll" altimg="si1.gif">DWw>(2n−1,hvariant="double-struck">F)w>h> is of subspace-type if and only if every hex hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si8.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=90b15733ae0f1d2f782679f261892fc1" title="Click to view the MathML source">FhContainer hidden">hCode">h id="mml8" overflow="scroll" altimg="si8.gif">Fh> of hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si1.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=90f9da144bfc69630b38688876bc4c52" title="Click to view the MathML source">DW(2n−1,F)hContainer hidden">hCode">h id="mml9" overflow="scroll" altimg="si1.gif">DWw>(2n−1,hvariant="double-struck">F)w>h> intersects it in either hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si8.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=90b15733ae0f1d2f782679f261892fc1" title="Click to view the MathML source">FhContainer hidden">hCode">h id="mml10" overflow="scroll" altimg="si8.gif">Fh>, a singular hyperplane of hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si8.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=90b15733ae0f1d2f782679f261892fc1" title="Click to view the MathML source">FhContainer hidden">hCode">h id="mml11" overflow="scroll" altimg="si8.gif">Fh> or the extension of a full subgrid of a quad. In the case hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si12.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=5db988cf78abcecff77cb8e6851c429f" title="Click to view the MathML source">FhContainer hidden">hCode">h id="mml12" overflow="scroll" altimg="si12.gif">hvariant="double-struck">Fh> is a perfect field of characteristic 2, a stronger result can be proved, namely a hyperplane hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si13.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=3e6287fba811e9222a8df087df01a1af" title="Click to view the MathML source">HhContainer hidden">hCode">h id="mml13" overflow="scroll" altimg="si13.gif">Hh> of hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si1.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=90f9da144bfc69630b38688876bc4c52" title="Click to view the MathML source">DW(2n−1,F)hContainer hidden">hCode">h id="mml14" overflow="scroll" altimg="si1.gif">DWw>(2n−1,hvariant="double-struck">F)w>h> is of subspace-type or arises from the spin-embedding of hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si15.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=d0e6a587e2c13447aaf45af289c61072" title="Click to view the MathML source">DW(2n−1,F)≅DQ(2n,F)hContainer hidden">hCode">h id="mml15" overflow="scroll" altimg="si15.gif">DWw>(2n−1,hvariant="double-struck">F)w>≅DQw>(2n,hvariant="double-struck">F)w>h> if and only if every hex hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si8.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=90b15733ae0f1d2f782679f261892fc1" title="Click to view the MathML source">FhContainer hidden">hCode">h id="mml16" overflow="scroll" altimg="si8.gif">Fh> intersects it in either hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si8.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=90b15733ae0f1d2f782679f261892fc1" title="Click to view the MathML source">FhContainer hidden">hCode">h id="mml17" overflow="scroll" altimg="si8.gif">Fh>, a singular hyperplane of hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si8.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=90b15733ae0f1d2f782679f261892fc1" title="Click to view the MathML source">FhContainer hidden">hCode">h id="mml18" overflow="scroll" altimg="si8.gif">Fh>, a hexagonal hyperplane of hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302357&_mathId=si8.gif&_user=111111111&_pii=S0012365X16302357&_rdoc=1&_issn=0012365X&md5=90b15733ae0f1d2f782679f261892fc1" title="Click to view the MathML source">FhContainer hidden">hCode">h id="mml19" overflow="scroll" altimg="si8.gif">Fh> or the extension of a full subgrid of a quad.