Disciplines
Mathematics (100%)
Keywords
-
Infinite-dimensional groups,
Quasi-Invariant Measures,
Symmetric Spaces,
Infinite Symmetric Groups,
Double Cosets
The research will follows several lines: 1. I intend to investigate multplication of double cosets on infinite-dimensional groups. 2. I want to investigate representations of infinite symmetric groups. 3. I hope to apply multiplication of double cosets to geometry and amaysis on finite-dimensional spaces. 4. I wish to investigate quasiinvariant actions of groups diffeomorphisms and hierarchomorphisms and corrersponding representations. 5. I intend to investigate polymorphisms related to infinite-dimensional groups. 6. I want to examine difference operators in imaginary direction and related multi-variate differential-difference operators. 7. I intend to continue my work on analysis on symmetric spaces. 8. I want to examine the analysis on inverse limits of symmetric spaces. 9. I want to examine braid groups and the corresponding Lie groups.
1. Sufficient spectral data for double cosets of infinite dimensional classical groups were obtained2. There were obtained a big family of functors producing topological field theory type constructions from representations of infinite symmetric groups. In particular, where were obtained simplicial 'topological field theories' of arbitrary dimension.3. There were obtained explicit formulas for action of the general linear Lie algebra in spectral decompositions of restriction of representations to a smaller subalgebra/4. Analogs of Hua measures and Hua integrals for flag spaces were constructed.5. Mapping class groups of diffeomorphisms preserving a Cantor set were examined.6. It is proved that the subgroup SL(2) is spherical in the group of diffeomorphisms of circles7. A family of spherical representations of a combinatorial analog of the group of diffeomorphisms of the cirle is constructed.8. Closures of some actions of infinite orthogonal group were obtained.
Research institution(s)
- Universität Wien - 100%
International project participants
Research Output
- 74 Citations
- 54 Publications
Publications
-
2016
Title The group of diffeomorphisms of the circle: reproducing kernels and analogs of spherical functions DOI 10.48550/arxiv.1601.02148 Type Preprint Author Neretin Y -
2016
Title On $p$-adic colligations and 'rational maps' of Bruhat-Tits trees. Type Book Chapter -
2016
Title ? ??????????? ????????? $\operatorname{PSL}_2(\mathbb R)$ ? ?????? ??????????????? ??????????: On the Sphericity of the Subgroup $\operatorname{PSL}_2(\mathbb{R})$ in the Group of Diffeomorphisms of the Circle DOI 10.4213/faa3227 Type Journal Article Author Neretin Y Journal ?????????????? ?????? ? ??? ?????????? Pages 91-94 Link Publication -
2021
Title Groups GL(8) over finite fields and multiplications of double cosets DOI 10.1016/j.jalgebra.2021.06.011 Type Journal Article Author Neretin Y Journal Journal of Algebra Pages 370-421 Link Publication -
2021
Title On spherical unitary representations of groups of spheromorphisms of Bruhat–Tits trees DOI 10.4171/ggd/612 Type Journal Article Author Neretin Y Journal Groups, Geometry, and Dynamics Pages 801-824 Link Publication -
2015
Title Matrix Beta-integrals: An Overview DOI 10.1007/978-3-319-18212-4_20 Type Book Chapter Author Neretin Y Publisher Springer Nature Pages 257-272 -
2015
Title Infinite symmetric groups and combinatorial constructions of topological field theory type DOI 10.1070/rm2015v070n04abeh004958 Type Journal Article Author Neretin Y Journal Russian Mathematical Surveys Pages 715-773 Link Publication -
2015
Title ???????????????? $p$-????????? ??????, ?????????? ??????? ??????? ????????? ? ?????????? ??????? ?? ????????? ????-?????: Infinite-dimensional $p$-adic groups, semigroups of double cosets, and inner functions on Bruhat-Tits buildings DOI 10.4213/im8299 Type Journal Article Author Neretin Y Journal ???????? ?????????? ???????? ????. ????? ?????????????? Pages 87-130 Link Publication -
2017
Title Projections Separating Spectra for $\boldsymbol{L^2}$ on Pseudounitary Groups $\boldsymbol{{\mathrm U}(p,q)}$ DOI 10.1093/imrn/rnx268 Type Journal Article Author Neretin Y Journal International Mathematics Research Notices Pages 5256-5283 Link Publication -
2017
Title Projectors separating spectra for $L^2$ on pseudounitary groups $U(p,q)$ DOI 10.48550/arxiv.1703.08814 Type Preprint Author Neretin Y -
2017
Title Projectors separating spectra for $L^2$ on symmetric spaces $GL(n,\C)/GL(n,\R)$ DOI 10.48550/arxiv.1704.00049 Type Preprint Author Neretin Y -
2017
Title Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument: ????????? ??????? ?????????????, ??????????? ???? ? ?????????????????? ??????? ?????????? ????????? DOI 10.4213/faa3441 Type Journal Article Author Neretin Y Journal ?????????????? ?????? ? ??? ?????????? Pages 25-41 Link Publication -
2017
Title Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument DOI 10.1007/s10688-017-0172-5 Type Journal Article Author Neretin Y Journal Functional Analysis and Its Applications Pages 98-111 -
2017
Title The group of diffeomorphisms of the circle: Reproducing kernels and analogs of spherical functions DOI 10.3934/jgm.2017009 Type Journal Article Author Neretin Y Journal Journal of Geometric Mechanics Pages 207-225 Link Publication -
2017
Title The Whishart–Pickrell Distributions and Closures of Group Actions DOI 10.1007/s10958-017-3417-1 Type Journal Article Author Neretin Y Journal Journal of Mathematical Sciences Pages 328-334 -
2016
Title On the sphericity of the subgroup PSL2(R) in the group of diffeomorphisms of the circle DOI 10.1007/s10688-016-0143-2 Type Journal Article Author Neretin Y Journal Functional Analysis and Its Applications Pages 160-162 -
2018
Title Infinite symmetric group, pseudomanifolds, and combinatorial cobordism-like structures DOI 10.1142/s179352531850022x Type Journal Article Author Gaifullin A Journal Journal of Topology and Analysis Pages 605-625 Link Publication -
2018
Title Diffeomorphism groups of tame Cantor sets and Thompson-like groups DOI 10.1112/s0010437x18007066 Type Journal Article Author Funar L Journal Compositio Mathematica Pages 1066-1110 Link Publication -
2018
Title Restriction of Representations of GL (n + 1, C) to GL (n, C) and Action of the Lie Overalgebra DOI 10.1007/s10468-018-9774-8 Type Journal Article Author Neretin Y Journal Algebras and Representation Theory Pages 1087-1117 Link Publication -
2020
Title Groups $GL(\infty)$ over finite fields and multiplications of double cosets DOI 10.48550/arxiv.2002.09969 Type Preprint Author Neretin Y -
2019
Title On spherical unitary representations of groups of spheromorphisms of Bruhat--Tits trees DOI 10.48550/arxiv.1906.12197 Type Preprint Author Neretin Y -
2014
Title The Lagrangian Radon Transform and the Weil Representation DOI 10.1007/s00041-013-9315-0 Type Journal Article Author Marmo G Journal Journal of Fourier Analysis and Applications Pages 321-361 -
2014
Title On an Infinite-Dimensional Limit of the Steinberg Representations DOI 10.1007/s10958-014-1963-3 Type Journal Article Author Neretin Y Journal Journal of Mathematical Sciences Pages 718-721 Link Publication -
2014
Title ?????????????? ??????? ?? ?????? ??????????????, ??????????? ???? ????????????????? DOI 10.4213/sm8339 Type Journal Article Author ??????? ? Journal ?????????????? ??????? Pages 145-160 Link Publication -
2016
Title On p-adic Colligations and ‘Rational Maps’ of Bruhat–Tits Trees DOI 10.1007/978-3-319-31756-4_14 Type Book Chapter Author Neretin Y Publisher Springer Nature Pages 139-158 -
2016
Title Geometric Methods in Physics, XXXIV Workshop, Bialowieza, Poland, June 28 – July 4, 2015 DOI 10.1007/978-3-319-31756-4 Type Book Publisher Springer Nature -
2016
Title Wishart--Pickrell distributions and closures of group actions DOI 10.48550/arxiv.1602.03492 Type Preprint Author Neretin Y -
2016
Title Several Remarks on Groups of Automorphisms of Free Groups DOI 10.1007/s10958-016-2880-4 Type Journal Article Author Neretin Y Journal Journal of Mathematical Sciences Pages 748-754 -
2015
Title Infinite symmetric groups and combinatorial constructions of topological field theory type: ??????????? ?????????????? ?????? ? ????????????? ??????????? ???? ?????????????? ?????? ???? DOI 10.4213/rm9667 Type Journal Article Author Neretin Y Journal Uspekhi Matematicheskikh Nauk Pages 143-204 Link Publication -
2015
Title Infinite-dimensional -adic groups, semigroups of double cosets, and inner functions on Bruhat–Tits buildings DOI 10.1070/im2015v079n03abeh002752 Type Journal Article Author Neretin Y Journal Izvestiya: Mathematics Pages 512-553 Link Publication -
2015
Title Infinite symmetric groups and combinatorial constructions of topological field theory type DOI 10.48550/arxiv.1502.03472 Type Preprint Author Neretin Y -
2015
Title Restriction of representations of $GL(n+1,C)$ to $GL(n,C)$ and action of the Lie overalgebra DOI 10.48550/arxiv.1510.03611 Type Preprint Author Neretin Y -
2015
Title Topological groups and invariant measures DOI 10.48550/arxiv.1510.03082 Type Preprint Author Neretin Y -
2015
Title Infinite symmetric group and bordisms of pseudomanifolds DOI 10.48550/arxiv.1501.04062 Type Preprint Author Gaifullin A -
2015
Title The subgroup $PSL(2,R)$ is spherical in the group of diffeomorphisms of the circle DOI 10.48550/arxiv.1501.05820 Type Preprint Author Neretin Y -
2013
Title On $p$-adic colligations and 'rational maps' of Bruhat-Tits trees DOI 10.48550/arxiv.1301.5453 Type Preprint Author Neretin Y -
2013
Title On multiplication of double cosets for $\GL(\infty)$ over a finite field DOI 10.48550/arxiv.1310.1596 Type Preprint Author Neretin Y -
2013
Title Several remarks on groups of automorphisms of free groups DOI 10.48550/arxiv.1306.6035 Type Preprint Author Neretin Y -
2013
Title Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II DOI 10.1007/s10455-013-9370-4 Type Journal Article Author Bauer M Journal Annals of Global Analysis and Geometry Pages 361-368 -
2015
Title Infinite-dimensional $p$-adic groups, semigroups of double cosets, and inner functions on Bruhat--Tits builldings. Type Journal Article Author Neretin Ya -
2015
Title Hua-Type Beta-Integrals and Projective Systems of Measures on Flag Spaces DOI 10.1093/imrn/rnv031 Type Journal Article Author Neretin Y Journal International Mathematics Research Notices Pages 11289-11301 Link Publication -
2014
Title Bi-invariant functions on the group of transformations leaving a measure quasi-invariant DOI 10.1070/sm2014v205n09abeh004421 Type Journal Article Author Neretin Y Journal Sbornik: Mathematics Pages 1357-1372 Link Publication -
2014
Title Diffeomorphisms groups of tame Cantor sets and Thompson-like groups DOI 10.48550/arxiv.1411.4855 Type Preprint Author Funar L -
2014
Title Matrix beta-integrals: an overview DOI 10.48550/arxiv.1411.2110 Type Preprint Author Neretin Y -
2014
Title On infinite-dimensional limit of the Steinberg representations DOI 10.48550/arxiv.1406.6535 Type Preprint Author Neretin Y -
2014
Title Hua type beta-integrals and projective systems of measures on flag spaces DOI 10.48550/arxiv.1406.6997 Type Preprint Author Neretin Y -
2014
Title Biinvariant functions on the group of transformations leaving a measure quasiinvariant DOI 10.48550/arxiv.1406.7251 Type Preprint Author Neretin Y -
0
Title Multiplication of conjugacy classes, colligations, and characteristic functions of matrix Argument. Type Other Author Neretin Ya -
0
Title Diffeomorphisms groups of Cantor sets and Thompson-type groups. Type Other Author Funar L -
0
Title Wishart--Pickrell distributions and closures of group Actions. Type Other Author Neretin Ya -
0
Title Infinite symmetric group and bordisms of pseudomanifolds. Type Other Author Gaifullin Aa -
0
Title On multiplication of double cosets for $GL(infty)$ over a finite field. Type Other Author Neretin Ya -
0
Title Topological groups and invariant measures. (lecture notes in Russian). Type Other Author Neretin Ya -
0
Title Restriction of representations of $GL(n+1,C)$ to $GL(n,C)$ and action of the Lie overalgebra. Type Other Author Neretin Ya