Let k be a local field.Let I_(v) and I_(v′)be smooth principal series representations of GLn(k)and GL_(n-1)(k),respectively.The Rankin-Selberg integrals yield a continuous bilinear map I_(v)×I_(v′)→C with a ce...Let k be a local field.Let I_(v) and I_(v′)be smooth principal series representations of GLn(k)and GL_(n-1)(k),respectively.The Rankin-Selberg integrals yield a continuous bilinear map I_(v)×I_(v′)→C with a certain invariance property.We study integrals over a certain open orbit that also yield a continuous bilinear map I_(v)×I_(v′)→C with the same invariance property and show that these integrals equal the Rankin-Selberg integrals up to an explicit constant.Similar results are also obtained for Rankin-Selberg integrals for GLn(k)×GLn(k).展开更多
A Nash group is said to be almost linear if it has a Nash representation with a finite kernel. Structures and basic properties of these groups are studied.
We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups.
Let k be a local field of characteristic zero.Letπbe an irreducible admissible smooth representation of GL2 n(k).We prove that for all but countably many charactersχ’s of GLn(k)×GLn(k),the space ofχ-equivaria...Let k be a local field of characteristic zero.Letπbe an irreducible admissible smooth representation of GL2 n(k).We prove that for all but countably many charactersχ’s of GLn(k)×GLn(k),the space ofχ-equivariant(continuous in the archimedean case)linear functionals onπis at most one dimensional.Using this,we prove the uniqueness of twisted Shalika models.展开更多
Given an arithmetic lattice of the unitary group U(3,1)arising from a hermitian form over a CM-field,we show that all unitary representations of U(3,1)with nonzero cohomology contribute to the cohomology of the attach...Given an arithmetic lattice of the unitary group U(3,1)arising from a hermitian form over a CM-field,we show that all unitary representations of U(3,1)with nonzero cohomology contribute to the cohomology of the attached arithmetic complex 3-manifold,at least when we pass to a finite-index subgroup of the given arithmetic lattice.展开更多
基金supported by the Natural Science Foundation of Zhejiang Province(Grant No.LZ22A010006)National Natural Science Foundation of China(Grant No.12171421)+2 种基金Feng Su was supported by National Natural Science Foundation of China(Grant No.11901466)the Qinglan Project of Jiangsu Provincesupported by the National Key Research and Development Program of China(Grant No.2020YFA0712600).
文摘Let k be a local field.Let I_(v) and I_(v′)be smooth principal series representations of GLn(k)and GL_(n-1)(k),respectively.The Rankin-Selberg integrals yield a continuous bilinear map I_(v)×I_(v′)→C with a certain invariance property.We study integrals over a certain open orbit that also yield a continuous bilinear map I_(v)×I_(v′)→C with the same invariance property and show that these integrals equal the Rankin-Selberg integrals up to an explicit constant.Similar results are also obtained for Rankin-Selberg integrals for GLn(k)×GLn(k).
基金supported by the National Natural Science Foundation of China(Nos.11222101,11321101)
文摘A Nash group is said to be almost linear if it has a Nash representation with a finite kernel. Structures and basic properties of these groups are studied.
基金supported by Research Grants Council General Research Fund of Hong Kong Special Administrative Region (Grant No. 16303314)supported by National Natural Science Foundation of China (Grant Nos. 11688101, 11525105, 11621061 and 11531008)
文摘We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups.
基金supported by National Natural Science Foundation of China(Grant No.11501478)The second author was supported by National Natural Science Foundation of China(Grant Nos.11525105,11688101,11621061 and 11531008)
文摘Let k be a local field of characteristic zero.Letπbe an irreducible admissible smooth representation of GL2 n(k).We prove that for all but countably many charactersχ’s of GLn(k)×GLn(k),the space ofχ-equivariant(continuous in the archimedean case)linear functionals onπis at most one dimensional.Using this,we prove the uniqueness of twisted Shalika models.
基金J.-S.Li was supported in part by RGC-GRF grant 602410 of HKSAR.B.Sun was supported in part by NSFC Grant 11222101.
文摘Given an arithmetic lattice of the unitary group U(3,1)arising from a hermitian form over a CM-field,we show that all unitary representations of U(3,1)with nonzero cohomology contribute to the cohomology of the attached arithmetic complex 3-manifold,at least when we pass to a finite-index subgroup of the given arithmetic lattice.
