Enhanced adjoint actions and their orbits for the general linear group
نویسندگان
چکیده
منابع مشابه
Adjoint and Coadjoint Orbits of the Poincaré Group
In this paper we give an effective method for finding a unique representative of each orbit of the adjoint and coadjoint action of the real affine orthogonal group on its Lie algebra. In both cases there are orbits which have a modulus that is different from the usual invariants for orthogonal groups. We find an unexplained bijection between adjoint and coadjoint orbits. As a special case, we c...
متن کاملNilpotent Orbits, Normality, and Hamiltonian Group Actions
Let M be a G-covering of a nilpotent orbit in 0 where G isa complex semisimple Lie group and g = Lie(G). We prove that under Poisson bracket the space R[2] of homogeneous functions on M of degree 2 is the unique maximal semisimple Lie subalgebra of R = R{M) containing g . The action of g' ~ R[2] exponentiates to an action of the corresponding Lie group G' on a G'-cover M' of a nilpotent orbit i...
متن کاملQuantum Co-adjoint Orbits of the Real Diamond Group
We present explicit formulas for deformation quantization on the coadjoint orbits of the real diamond Lie group. From this we obtain quantum halfplans, quantum hyperbolic cylinders, quantum hyperbolic paraboloids via Fedosov deformation quantization and finally, the corresponding unitary representations of this group.
متن کاملConnections for general group actions
Principal bundles serve as a powerful and elegant geometric framework for analyzing group actions and symmetry. Beyond their geometric origins, principal bundles play significant roles in the analysis of mechanical systems with symmetry, as well as the design of appropriate computational algorithms. A connection on a principal bundle is defined as an equivariant decomposition of vectors into in...
متن کاملRegularisable and Minimal Orbits for Group Actions in Infinite Dimensions
We introduce a class of regularisable infinite dimensional principal fibre bundles which includes fibre bundles arising in gauge field theories like Yang-Mills and string theory and which generalise finite dimensional Riemannian principal fibre bundles induced by an isometric action. We show that the orbits of regularisable bundles have well defined, both heat-kernel and zeta function regularis...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2019
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2019.298.141