This memoir investigates a method that generalizes the Chern-Federer kinematic formula to arbitrary homogeneous spaces with an invariant Riemannian metric, and leads to new formulas even in the case of submanifolds of Euclidean space.
This paper is largely devoted to the behaviour of operators which are polynomials (in several variables) in full and one-sided shifts, together with their corresponding Toeplitz operators, with consequences for product type actions of compact connected Lie groups. Problems are o…
Topological Galois Theory
by Hovanskij, Askol'd Georgievič
fromSpringer Monographs in Mathematics
This work comprises a general study of symmetry breaking for compact Lie groups in the context of equivariant bifurcation theory. We begin by extending the theory developed by Field and Richardson for absolutely irreducible representations of finite groups to general irreducible…
The category of highest weight representations is of special interest withing the full set of representations of a real semisimple Lie group. This memoir describes the structure of the generalized Verma modules as well as the Kazhdan-Lusztig data for the simple modules in this c…
The Selberg trace formula reduces the problem of calculating the dimension of cusp forms of Siegal upper-half space, when the fundamental domain is not compact but has finite volume, to the evaluation of certain integrals combining with special values of certain zeta functions. …
The first part of this paper constructs a class of naturally reductive metrics on compact Lie groups and shows that all naturally reductive left invariant metrics are of this type if the group is simple. The second part analyzes the question of when these metrics are Einstein an…
Our work is aimed toward an understanding of higher-order extension groups in the category of ([bold italic]g, [bold italic]K)-modules. Although our final results concern rank one Lie groups, the ideas and approach are applicable to any semisimple matrix group.
