Eichler-Shimura isomorphism for complex hyperbolic lattices

被引：1

作者：

Kim, Inkang ^{[1
]}

Zhang, Genkai ^{[2
]}

机构：

[1] KIAS, Sch Math, Heogiro 85, Seoul 130722, South Korea

[2] Gothenburg Univ, Chalmers Univ Technol & Math Sci, Math Sci, SE-41296 Gothenburg, Sweden

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2017年 / 121卷

关键词：

Complex hyperbolic lattice; First cohomology; Eichler-Shimura isomorphism; PROJECTIVE-STRUCTURES; LOCAL RIGIDITY; LIE-GROUPS; SPACE; COHOMOLOGY;

D O I：

10.1016/j.geomphys.2017.08.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the cohomology group H-1(Gamma, p) of a discrete subgroup Gamma subset of G = SU(n, 1) and the symmetric tensor representation p on S-m(c(n+1)). We give an elementary proof of the Eichler-Shimura isomorphism that harmonic forms H-1(Gamma\ G/K, p) are (0, 1)-forms for the automorphic holomorphic bundle induced by the representation S-m(C-n) of K. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：452 / 460

页数：9

共 50 条

[21] Complex hyperbolic lattices
Parker, John R.
DISCRETE GROUPS AND GEOMETRIC STRUCTURES, 2009, 501 : 1 - 42
[22] Eichler–Shimura theory for mock modular forms
Kathrin Bringmann
Pavel Guerzhoy
Zachary Kent
Ken Ono
Mathematische Annalen, 2013, 355 : 1085 - 1121
[23] On Shimura, Shintani and Eichler-Zagier correspondences
Manickam, M
Ramakrishnan, B
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (06) : 2601 - 2617
[24] The Eichler–Shimura cohomology theorem for Jacobi forms
Dohoon Choi
Subong Lim
Monatshefte für Mathematik, 2017, 182 : 271 - 288
[25] On representations of complex hyperbolic lattices
Wang, M
MATHEMATICAL RESEARCH LETTERS, 1999, 6 (01) : 99 - 105
[26] Complex hyperbolic orbifolds and hybrid lattices
Falbel, Elisha
Pasquinelli, Irene
GEOMETRIAE DEDICATA, 2023, 217 (02)
[27] Complex hyperbolic orbifolds and hybrid lattices
Elisha Falbel
Irene Pasquinelli
Geometriae Dedicata, 2023, 217
[28] Zeta-polynomials, Hilbert polynomials, and the Eichler–Shimura identities
Marie Jameson
Research in the Mathematical Sciences, 2019, 6
[29] Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices
Isenrich, Claudio Llosa
Py, Pierre
INVENTIONES MATHEMATICAE, 2023, 235 (1) : 233 - 254
[30] Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices
Claudio Llosa Isenrich
Pierre Py
Inventiones mathematicae, 2024, 235 : 233 - 254

← 1 2 3 4 5 →