Generalized Picard lattices arising from half-integral conditions
G. D. Mostow (1986)
Publications Mathématiques de l'IHÉS
Peter Franek (2006)
Archivum Mathematicum
In this paper we study invariant differential operators on manifolds with a given parabolic structure. The model for the parabolic geometry is the quotient of the orthogonal group by a maximal parabolic subgroup corresponding to crossing of the -th simple root of the Dynkin diagram. In particular, invariant differential operators discussed in the paper correspond (in a flat model) to the Dirac operator in several variables.
J. Lepowsky (1979)
Annales scientifiques de l'École Normale Supérieure
Abdel-Ilah Benabdallah (1983)
Bulletin de la Société Mathématique de France
Abdel-Ilah Benabdallah (1982)
Publications du Département de mathématiques (Lyon)
T.T. Bowman (1972)
Semigroup forum
Golenistcheva-Kutuzova, M. I. (1991)
Proceedings of the Winter School "Geometry and Physics"
Ya'acov Peterzil, Anand Pillay (2007)
Fundamenta Mathematicae
A subset X of a group G is called left genericif finitely many left translates of X cover G. Our main result is that if G is a definably compact group in an o-minimal structure and a definable X ⊆ G is not right generic then its complement is left generic. Among our additional results are (i) a new condition equivalent to definable compactness, (ii) the existence of a finitely additive invariant measure on definable sets in a definably compact group G in the case where G = *H...
Stephen S. Kudla, John J. Millson (1982)
Compositio Mathematica
Figula, Ágota (2000)
Journal of Lie Theory
Bromberg, Shirley, Medina, Alberto (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Neda Bokan, Tijana Šukilović, Srdjan Vukmirović (2019)
Czechoslovak Mathematical Journal
Two metrics on a manifold are geodesically equivalent if the sets of their unparameterized geodesics coincide. We show that if two -invariant metrics of arbitrary signature on homogenous space are geodesically equivalent, they are affinely equivalent, i.e. they have the same Levi-Civita connection. We also prove that the existence of nonproportional, geodesically equivalent, -invariant metrics on homogenous space implies that their holonomy algebra cannot be full. We give an algorithm for...
Berenice Guerrero (1990)
Revista colombiana de matematicas
Gleb Arutyunov (1997)
Banach Center Publications
By applying the Hamiltonian reduction technique we derive a matrix first order differential equation that yields the classical r-matrices of the elliptic (Euler-) Calogero-Moser systems as well as their degenerations.
Wolf, Joseph A. (1991)
Proceedings of the Winter School "Geometry and Physics"
[For the entire collection see Zbl 0742.00067.]Let be a connected semisimple Lie group with finite center. In this review article the author describes first the geometric realization of the discrete series representations of on Dolbeault cohomology spaces and the tempered series of representations of on partial Dolbeault cohomology spaces. Then he discusses his joint work with Wilfried Schmid on the construction of maximal globalizations of standard Zuckerman modules via geometric quantization....
Peter Heinzner (1991)
Mathematische Annalen
Tammo tom Dieck, Ted Petrie (1978)
Inventiones mathematicae
William D. Dunbar (1988)
Revista Matemática de la Universidad Complutense de Madrid
An orbifold is a topological space which ?locally looks like? the orbit space of a properly discontinuous group action on a manifold. After a brief review of basic concepts, we consider the special case 3-dimensional orbifolds of the form GammaM, where M is a simply-connected 3-dimensional homogeneous space corresponding to one of Thurston?s eight geometries, and where Gamma < Isom(M) acts properly discontinuously. A general description of these geometric orbifolds is given and the closed...
V. Guillemin, S. Sternberg (1982)
Inventiones mathematicae
Y.L. Tong, S.P. Wang (1989)
Inventiones mathematicae