Determinants of Sum of Orbits under Compact Lie Group
نویسندگان
چکیده
We study the determinants on the sum of orbits of two elements in the Lie algebra of a compact connected subgroup in the unitary group. As an application, the extremal determinant expressions are obtained for the symplectic group.
منابع مشابه
Orbit Spaces Arising from Isometric Actions on Hyperbolic Spaces
Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology. Dimension of is called the cohomogeneity of the action of on . If is a differentiable manifold of cohomogeneity one under the action of a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...
متن کاملDistinguished Orbits and the L-s Category of Simply Connected Compact Lie Groups
We show that the Lusternik-Schnirelmann category of a simple, simply connected, compact Lie group G is bounded above by the sum of the relative categories of certain distinguished conjugacy classes in G corresponding to the vertices of the fundamental alcove for the action of the affine Weyl group on the Lie algebra of a maximal torus of G.
متن کاملSums of Adjoint Orbits
We show that the sum of two adjoint orbits in the Lie algebra of an exponential Lie group coincides with the Campbell-Baker-Hausdorff product of these two orbits. Introduction N. Wildberger and others have recently investigated the structure of the hypergroup of the adjoint orbits in relation with the class hypergroup of compact Lie groups. A generalization of the notion of this type of hypergr...
متن کاملSUMS OF ADJOINT ORBITS AND L–SINGULAR DICHOTOMY FOR SU(m)
Let G be a real compact connected simple Lie group, and g its Lie algebra. We study the problem of determining, from root data, when a sum of adjoint orbits in g, or a product of conjugacy classes in G, contains an open set. Our general methods allow us to determine exactly which sums of adjoint orbits in su(m) and products of conjugacy classes in SU(m) contain an open set, in terms of the high...
متن کاملThe Orbit Method and Gelfand Pairs Associated with Nilpotent Lie Groups
Let K be a compact Lie group acting by automorphisms on a nilpotent Lie group N . One calls (K,N) a Gelfand pair when the integrable K-invariant functions on N form a commutative algebra under convolution. We prove that in this case the coadjoint orbits for G := K nN which meet the annihilator k⊥ of the Lie algebra k of K do so in single K-orbits. This generalizes a result of the authors and R....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010