FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1831176968> ?p ?o ?g. }

• W1831176968 abstract "Suppose <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=2 n plus 1 greater-than-or-equal-to p plus q> <mml:semantics> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mi>p</mml:mi> <mml:mo>+</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>2n+1 geq p+q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In an earlier paper in 2000 we study a certain sesquilinear form <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis comma right-parenthesis Subscript pi> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>π<!-- π --></mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>(,)_{pi }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> introduced by Jian-Shu Li in 1989. For <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=pi> <mml:semantics> <mml:mi>π<!-- π --></mml:mi> <mml:annotation encoding=application/x-tex>pi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in the semistable range of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=theta left-parenthesis upper M upper O left-parenthesis p comma q right-parenthesis right-arrow upper M upper S p Subscript 2 n Baseline left-parenthesis double-struck upper R right-parenthesis right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>θ<!-- θ --></mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>M</mml:mi> <mml:mi>O</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mi>M</mml:mi> <mml:mi>S</mml:mi> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>theta (MO(p,q) rightarrow MSp_{2n}(mathbb {R}))</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis comma right-parenthesis Subscript pi> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>π<!-- π --></mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>(,)_{pi }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> does not vanish, then it induces a sesquilinear form on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=theta left-parenthesis pi right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>θ<!-- θ --></mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>π<!-- π --></mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>theta (pi )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In another work in 2000 we proved that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis comma right-parenthesis Subscript pi> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>π<!-- π --></mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>(,)_{pi }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is positive semidefinite under a mild growth condition on the matrix coefficients of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=pi> <mml:semantics> <mml:mi>π<!-- π --></mml:mi> <mml:annotation encoding=application/x-tex>pi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In this paper, we show that either <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis comma right-parenthesis Subscript pi> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>π<!-- π --></mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>(,)_{pi }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> or <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis comma right-parenthesis Subscript pi circled-times det> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>π<!-- π --></mml:mi> <mml:mo>⊗<!-- ⊗ --></mml:mo> <mml:mo movablelimits=true form=prefix>det</mml:mo> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>(,)_{pi otimes det }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is nonvanishing. These results combined with one result of Przebinda suggest the existence of certain unipotent representations of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M p Subscript 2 n Baseline left-parenthesis double-struck upper R right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>M</mml:mi> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>Mp_{2n}(mathbb {R})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> beyond unitary representations of low rank." @default.
• W1831176968 created "2016-06-24" @default.
• W1831176968 creator A5039461117 @default.
• W1831176968 date "2001-10-30" @default.
• W1831176968 modified "2023-09-23" @default.
• W1831176968 title "Nonvanishing of a certain sesquilinear form in the theta correspondence" @default.
• W1831176968 cites W1599617315 @default.
• W1831176968 cites W1980460898 @default.
• W1831176968 cites W2001888789 @default.
• W1831176968 cites W2022989206 @default.
• W1831176968 cites W2046961757 @default.
• W1831176968 cites W2069206585 @default.
• W1831176968 cites W2093262898 @default.
• W1831176968 cites W2139734935 @default.
• W1831176968 cites W4246077597 @default.
• W1831176968 cites W4253555555 @default.
• W1831176968 cites W91805531 @default.
• W1831176968 doi "https://doi.org/10.1090/s1088-4165-01-00140-6" @default.
• W1831176968 hasPublicationYear "2001" @default.
• W1831176968 type Work @default.
• W1831176968 sameAs 1831176968 @default.
• W1831176968 citedByCount "7" @default.
• W1831176968 countsByYear W18311769682020 @default.
• W1831176968 crossrefType "journal-article" @default.
• W1831176968 hasAuthorship W1831176968A5039461117 @default.
• W1831176968 hasBestOaLocation W18311769681 @default.
• W1831176968 hasConcept C136119220 @default.
• W1831176968 hasConcept C138885662 @default.
• W1831176968 hasConcept C163353815 @default.
• W1831176968 hasConcept C202444582 @default.
• W1831176968 hasConcept C33923547 @default.
• W1831176968 hasConcept C41895202 @default.
• W1831176968 hasConcept C94940 @default.
• W1831176968 hasConceptScore W1831176968C136119220 @default.
• W1831176968 hasConceptScore W1831176968C138885662 @default.
• W1831176968 hasConceptScore W1831176968C163353815 @default.
• W1831176968 hasConceptScore W1831176968C202444582 @default.
• W1831176968 hasConceptScore W1831176968C33923547 @default.
• W1831176968 hasConceptScore W1831176968C41895202 @default.
• W1831176968 hasConceptScore W1831176968C94940 @default.
• W1831176968 hasLocation W18311769681 @default.
• W1831176968 hasOpenAccess W1831176968 @default.
• W1831176968 hasPrimaryLocation W18311769681 @default.
• W1831176968 hasRelatedWork W1554316026 @default.
• W1831176968 hasRelatedWork W1556698389 @default.
• W1831176968 hasRelatedWork W1585454614 @default.
• W1831176968 hasRelatedWork W191239096 @default.
• W1831176968 hasRelatedWork W1919732361 @default.
• W1831176968 hasRelatedWork W1924109525 @default.
• W1831176968 hasRelatedWork W1983599425 @default.
• W1831176968 hasRelatedWork W1987513039 @default.
• W1831176968 hasRelatedWork W2001889548 @default.
• W1831176968 hasRelatedWork W2069206585 @default.
• W1831176968 hasRelatedWork W2070342499 @default.
• W1831176968 hasRelatedWork W2081525104 @default.
• W1831176968 hasRelatedWork W2087554234 @default.
• W1831176968 hasRelatedWork W2094819090 @default.
• W1831176968 hasRelatedWork W2152689061 @default.
• W1831176968 hasRelatedWork W2254284813 @default.
• W1831176968 hasRelatedWork W2951123032 @default.
• W1831176968 hasRelatedWork W2951932840 @default.
• W1831176968 hasRelatedWork W2963061374 @default.
• W1831176968 hasRelatedWork W3103350712 @default.
• W1831176968 isParatext "false" @default.
• W1831176968 isRetracted "false" @default.
• W1831176968 magId "1831176968" @default.
• W1831176968 workType "article" @default.