Inspired by work of Enright andWillenbring [EW], we prove a generalized Littlewood’s restriction formula in terms of Dirac cohomology. Our approach is to use a character formula of irreducible unitary lowest weight modules instead of the Bernstein-Gelfand-Gelfand resolution, and the proof is much simpler. We also show that our branching formula is equivalent to the formula of Enright and Willen...

Up to equivalence, this paper classifies all the irreducible unitary representations with non-zero Dirac cohomology for simple Lie group $E_{6(-14)}$, which is of Hermitian symmetric type. Each FS-scattered series $E_{6(-14)}$ realized as a composition factor certain $A_{\mathfrak{q}}(\lambda)$ module. Along way, we have also obtained fully supported integral infinitesimal characters.

The existence of admissible vectors for a locally compact group is closely related to the group's profile. In the compact groups, according to Peter-weyl theorem, every irreducible representation has admissible vector. In this paper, the conditions under which the inverse of this case is being investigated has been investigated. Conditions such as views that are admissible and stable will get c...

It is well-known that unitary irreducible representations of groups can be usefully classified in a 3-fold classification scheme: Real, Complex, Quaternionic. In 1962 Freeman Dyson pointed out there an analogous 10-fold involving both and antiunitary operators. More recently it was realized also scheme superdivision algebras. Here we give careful proof the equivalence these two ways.

We give an operator theoretic approach to the constructions of multiresolutions as they are used in a number of basis constructions with wavelets, and in Hilbert spaces on fractals. Our approach starts with the following version of the classical Baumslag-Solitar relations ut = tu where t is a unitary operator in a Hilbert space H and u is an isometry in H. There are isometric dilations of this ...

We complete the classification of symmetry constraints on gapped quadratic fermion hamiltonians proposed by Kitaev. The symmetry group is supposed compact and can include arbitrary unitary or antiunitary operators in the Fock space that conserve the algebra of quadratic observables. We analyze the multiplicity spaces of real irreducible representations of unitary symmetries in the Nambu space. ...

We present the dictionary between one-particle Hilbert spaces of totally symmetric tensor-spinor fields spin $s={3}/{2}, {5}/{2}$ with any mass parameter on $D$-dimensional ($D \geq 3$) de Sitter space ($dS_{D}$) and Unitary Irreducible Representations (UIR's) algebra spin$(D,1)$. Our approach is based expressing eigenmodes global $dS_{D}$ in terms Dirac operator ${(D-1)}$-sphere, which provide...