Compact Simple Lie Groups and Their C-, S-, and E-Transforms
نویسندگان
چکیده
منابع مشابه
Compact Simple Lie Groups and Their C-, S-, and E-Transforms
New continuous group transforms, together with their discretization over a lattice of any density and admissible symmetry, are defined for a general compact simple Lie groups of rank 2 ≤ n < ∞. Rank 1 transforms are known. Rank 2 exposition of Cand S-transforms is in the literature. The E-transforms appear here for the first time.
متن کاملEquivariant Gerbes over Compact Simple Lie Groups
Using groupoid S-central extensions, we present, for a compact simple Lie group G, an infinite dimensional model of S-gerbe over the differential stack G/G whose Dixmier-Douady class corresponds to the canonical generator of the equivariant cohomology H G(G). c © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Gerbes Equivariantes sur les groupes de Lie simples compa...
متن کاملOrthogonal Polynomials of Compact Simple Lie Groups
Recursive algebraic construction of two infinite families of polynomials in n variables is proposed as a uniform method applicable to every semisimple Lie group of rank n. Its result recognizes Chebyshev polynomials of the first and second kind as the special case of the simple group of type A1. The obtained not Laurent-type polynomials are equivalent to the partial cases of theMacdonald symmet...
متن کاملBerry ’ s phase for compact Lie groups
The Lie group adiabatic evolution determined by a Lie algebra parameter dependent Hamiltonian is considered. It is demonstrated that in the case when the parameter space of the Hamiltonian is a homogeneous Kähler manifold its fundamental Kähler potentials completely determine Berry geometrical phase factor. Explicit expressions for Berry vector potentials (Berry connections) and Berry curvature...
متن کاملFinal Draft ON RADON TRANSFORMS ON COMPACT LIE GROUPS
We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to S nor to S. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms fr...
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: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2005
ISSN: 1815-0659
DOI: 10.3842/sigma.2005.025