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Symplectic convexity theorems and coadjoint orbits
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Structure and Geometry of Lie Groups
Matrix Groups.- Concrete Matrix Groups. The Matrix Exponential Function. Linear Lie Groups. Lie Algebras.- Elementary Structure Theory of Lie Algebras. Root Decomposition. Representation Theory of
Lie groups, convex cones, and semigroups
The geometry of cones wedges in Lie algebras invariant cones the local Lie theory of semigroups subsemigroups of Lie groups positivity embedding semigroups into Lie groups.
Lie semigroups and their applications
Lie semigroups and their tangent wedges.- Examples.- Geometry and topology of Lie semigroups.- Ordered homogeneous spaces.- Applications of ordered spaces to Lie semigroups.- Maximal semigroups in
Contraction of Hamiltonian $K$-spaces
In the spirit of recent work of Harada-Kaveh and Nishinou-Nohara-Ueda, we study the symplectic geometry of Popov's horospherical degenerations of complex algebraic varieties with the action of a
Basic Lie Theory
This chapter is devoted to the subject proper of this book: Lie groups, defined as smooth manifolds with a group structure such that all structure maps (multiplication and inversion) are smooth. Here
Linear Lie Groups
We call a closed subgroup \(G \subseteq \mathop {\mathrm {GL}}\nolimits _{n}({\mathbb{K}})\) a linear Lie group. In this section, we shall use the exponential function to assign to each linear Lie
A Lewis Correspondence for submodular groups
Abstract We extend the Lewis Correspondence between Maaß wave forms and period functions to subgroups of the modular group of finite index. The period functions then become vector valued functions.