Spherical analysis on harmonic groups
Spherical Functions and a q-Analogue of Kostant's Weight Multiplicity Formula.
Spherical functions and spectral synthesis
Spherical functions and uniformly bounded representations of free groups
We give a construction of an analytic series of uniformly bounded representations of a free group G, through the action of G on its Poisson boundary. These representations are irreducible and give as their coefficients all the spherical functions on G which tend to zero at infinity. The principal and the complementary series of unitary representations are included. We also prove that this construction and the other known constructions lead to equivalent representations.
Spherical functions are Fourier transforms of -functions
Spherical functions on a complex classical quantum group
Spherical Functions on a Simply Connected Semisimple Lie Group. II. The Paley-Wiener Theorem for the Rank one Case.
Spherical gradient manifolds
We study the action of a real-reductive group on a real-analytic submanifold of a Kähler manifold. We suppose that the action of extends holomorphically to an action of the complexified group on this Kähler manifold such that the action of a maximal compact subgroup is Hamiltonian. The moment map induces a gradient map . We show that almost separates the –orbits if and only if a minimal parabolic subgroup of has an open orbit. This generalizes Brion’s characterization of spherical...
Spherical harmonics on Grassmannians
We propose a generalization of the theory of spherical harmonics to the context of symmetric subgroups of reductive groups acting on flag manifolds. We give some sample results for the case of the orthogonal group acting on Grassmann manifolds, especially the case of 2-planes.
Spherical means on the Heisenberg group and a restriction theorem for the symplectic Fourier transform.
The aim of this paper is to study mean value operators on the reduced Heisenberg group Hn/Γ, where Hn is the Heisenberg group and Γ is the subgroup {(0,2πk): k ∈ Z} of Hn.
Spherical unitary dual of general linear group over non-Archimidean local field
Let be a local non-archimedean field. The set of all equivalence classes of irreducible spherical representations of is described in the first part of the paper. In particular, it is shown that each irreducible spherical representation is parabolically induced by an unramified character. Bernstein’s result on the irreducibility of the parabolically induced representations of by irreducible unitary ones, and Ol’shanskij’s construction of complementary series give directly a description of all...
Spin representations and binary numbers
We consider a construction of the fundamental spin representations of the simple Lie algebras in terms of binary arithmetic of fixed width integers. This gives the spin matrices as a Lie subalgebra of a -graded associative algebra (rather than the usual -filtered Clifford algebra). Our description gives a quick way to write down the spin matrices, and gives a way to encode some extra structure, such as the real structure which is invariant under the compact real form, for some . Additionally...
Spinc-quantization and the K-multiplicities of the discrete series
Spinorial matter and general relativity theory
Spinor-type fields with linear, affine and general coordinate transformations
Split ...-coextensions of topological inverse semigroups.
Splitting in locally compact abelian groups
Splitting of the identity component in locally compact abelian groups
Square integrability of group representations on homogeneous spaces. II. Coherent and quasi-coherent states. The case of the Poincaré group
Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames