Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces
We define a Toledo number for actions of surface groups and complex hyperbolic lattices on infinite dimensional Hermitian symmetric spaces, which allows us to define maximal representations. When the target is not of tube type we show that there cannot be Zariski-dense maximal representations, and w...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
24 Oct 2018
|
| In: |
Arxiv
|
| Online Access: | Verlag, Volltext: http://arxiv.org/abs/1810.10208
|
| Author Notes: | Bruno Duchesne, Jean Lécureux, and Maria Beatrice Pozzetti |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1587443759 | ||
| 003 | DE-627 | ||
| 005 | 20220815101836.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 190211s2018 xx |||||o 00| ||eng c | ||
| 035 | |a (DE-627)1587443759 | ||
| 035 | |a (DE-576)517443759 | ||
| 035 | |a (DE-599)BSZ517443759 | ||
| 035 | |a (OCoLC)1341037490 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Duchesne, Bruno |e VerfasserIn |0 (DE-588)1177716399 |0 (DE-627)1048870472 |0 (DE-576)517442639 |4 aut | |
| 245 | 1 | 0 | |a Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces |c Bruno Duchesne, Jean Lécureux, and Maria Beatrice Pozzetti |
| 264 | 1 | |c 24 Oct 2018 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Last revised 8 Nov 2018 (v2) | ||
| 500 | |a Gesehen am 11.02.2019 | ||
| 520 | |a We define a Toledo number for actions of surface groups and complex hyperbolic lattices on infinite dimensional Hermitian symmetric spaces, which allows us to define maximal representations. When the target is not of tube type we show that there cannot be Zariski-dense maximal representations, and whenever the existence of a boundary map can be guaranteed, the representation preserves a finite dimensional totally geodesic subspace on which the action is maximal. In the opposite direction we construct examples of geometrically dense maximal representation in the infinite dimensional Hermitian symmetric space of tube type and finite rank. Our approach is based on the study of boundary maps, that we are able to construct in low ranks or under some suitable Zariski-density assumption, circumventing the lack of local compactness in the infinite dimensional setting. | ||
| 650 | 4 | |a 20F67, 32M15 | |
| 650 | 4 | |a Mathematics - Differential Geometry | |
| 650 | 4 | |a Mathematics - Group Theory | |
| 700 | 1 | |a Lécureux, Jean |e VerfasserIn |0 (DE-588)1177717786 |0 (DE-627)104887141X |0 (DE-576)517443325 |4 aut | |
| 700 | 1 | |a Pozzetti, Maria Beatrice |d 1987- |e VerfasserIn |0 (DE-588)1138212202 |0 (DE-627)895519631 |0 (DE-576)492391424 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Arxiv |d Ithaca, NY : Cornell University, 1991 |g (2018) Artikel-Nummer 1810.10208, 50 Seiten |h Online-Ressource |w (DE-627)509006531 |w (DE-600)2225896-6 |w (DE-576)28130436X |7 nnas |a Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces |
| 773 | 1 | 8 | |g year:2018 |a Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces |
| 856 | 4 | 0 | |u http://arxiv.org/abs/1810.10208 |x Verlag |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20190211 | ||
| 993 | |a Article | ||
| 994 | |a 2018 | ||
| 998 | |g 1138212202 |a Pozzetti, Maria Beatrice |m 1138212202:Pozzetti, Maria Beatrice |d 110000 |d 110100 |d 110000 |d 110400 |e 110000PP1138212202 |e 110100PP1138212202 |e 110000PP1138212202 |e 110400PP1138212202 |k 0/110000/ |k 1/110000/110100/ |k 0/110000/ |k 1/110000/110400/ |p 3 |y j | ||
| 999 | |a KXP-PPN1587443759 |e 3055491572 | ||
| BIB | |a Y | ||
| JSO | |a {"name":{"displayForm":["Bruno Duchesne, Jean Lécureux, and Maria Beatrice Pozzetti"]},"id":{"eki":["1587443759"]},"language":["eng"],"person":[{"roleDisplay":"VerfasserIn","given":"Bruno","display":"Duchesne, Bruno","family":"Duchesne","role":"aut"},{"display":"Lécureux, Jean","roleDisplay":"VerfasserIn","given":"Jean","role":"aut","family":"Lécureux"},{"role":"aut","family":"Pozzetti","display":"Pozzetti, Maria Beatrice","roleDisplay":"VerfasserIn","given":"Maria Beatrice"}],"title":[{"title_sort":"Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces","title":"Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces"}],"recId":"1587443759","type":{"bibl":"chapter","media":"Online-Ressource"},"note":["Last revised 8 Nov 2018 (v2)","Gesehen am 11.02.2019"],"origin":[{"dateIssuedDisp":"24 Oct 2018","dateIssuedKey":"2018"}],"relHost":[{"part":{"text":"(2018) Artikel-Nummer 1810.10208, 50 Seiten","year":"2018","volume":"(2018) Artikel-Nummer 1810.10208","issue":"50 Seiten"},"title":[{"title":"Arxiv","title_sort":"Arxiv"}],"origin":[{"dateIssuedKey":"1991","publisher":"Cornell University ; Arxiv.org","publisherPlace":"Ithaca, NY ; [Erscheinungsort nicht ermittelbar]","dateIssuedDisp":"1991-"}],"pubHistory":["1991 -"],"type":{"bibl":"edited-book","media":"Online-Ressource"},"note":["Gesehen am 28.05.2024"],"physDesc":[{"extent":"Online-Ressource"}],"recId":"509006531","titleAlt":[{"title":"Arxiv.org"},{"title":"Arxiv.org e-print archive"},{"title":"Arxiv e-print archive"},{"title":"De.arxiv.org"}],"id":{"zdb":["2225896-6"],"eki":["509006531"]},"disp":"Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spacesArxiv","language":["eng"]}]} | ||
| SRT | |a DUCHESNEBRBOUNDARYMA2420 | ||