Related papers: Irreducible wavelet representations and ergodic au…
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
We consider dynamics of scalar semilinear parabolic equations on bounded intervals with periodic boundary conditions, and on the entire real line, with a general nonlinearity $g(t,x,u,u_x)$ either not depending on $t$, or periodic in $t$.…
In this paper we first determine all irreducible representations of a wedge product of two table algebras in terms of the irreducible representations of two factors involved. Then we give some necessary and sufficient conditions for a table…
A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum…
In this article we provide an identification between the wavelet decompositions of certain fractal representations of $C^*-$algebras of directed graphs of M. Marcolli and A. Paolucci, and the eigenspaces of Laplacians associated to spectral…
We consider the inverse problem of recovering a potential from the Dirichlet to Neumann map at a large fixed frequency on certain Riemannian manifolds. We extend the earlier result of [G. Uhlmann and Y. Wang, arXiv:2104.03477] to the case…
We provide two different proofs of an irreducibility criterion for the preimages of a transverse subvariety of a product of elliptic curves under a diagonal endomorphism of sufficiently large degree.For curves, we present an arithmetic…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
The transformation properties of irreducible tensor operators and the applicability of the Wigner-Eckart theorem to finite magnetic groups have been studied.
We obtain representations of $X_1$ exceptional orthogonal polynomials through determinants of matrices that have certain adjusted moments as entries. We start out directly from the Darboux transformation, allowing for a universal…
This is a tutorial introduction to the representation theory of SU(2) with emphasis on the occurrence of Jacobi polynomials in the matrix elements of the irreducible representations. The last section traces the history of the insight that…
This paper develops methods based on coarse geometry for the comparison of wavelet coorbit spaces defined by different dilation groups, with emphasis on establishing a unified approach to both irreducible and reducible quasi-regular…
The main purpose of this paper is providing a simple method to generate the matrices of irreducible representations because it is useful to reduce the computational time of solving the eigenvalue problems. The only information we need to…
Let $K$ be a connected compact semisimple group and $V_\lambda$ be an irreducible unitary representation with highest weight $\lambda$. We study the momentum map $\mu:\mathbb P(V_\lambda)\to\mathfrak k^*$. The intersection $\mu(\mathbb…
For infinite reductive groups with Frobenius maps, we show that certain subquotients of abstract representations of the groups induced from 1-dimensional representations of Borel subgroups are irreducible.
This paper proposes a new approach to deriving a finite particle content, suitable for the construction of a gauge theory. Specifically, the outlined construction generates a finite set of irreducible gauge representations, which are…
It is shown that the use of extended sets of irreducible representations of the Lorentz group opens new possibilities for the theory of relativistic wave equations from the point of view of the space-time description of both the internal…
We provide new insights into the solvability property of an Hamiltonian involving of the fourth Painlev\'e transcendent and its derivatives. This Hamiltonian is third order shape invariant and can also be interpreted within the context of…
The contributions to $S$, $T$, and $U$ from heavy scalars in any irreducible representation of the electroweak gauge group $SU(2)_L\times U(1)_Y$ are obtained. We find that in the case of a heavy scalar doublet there is a slight difference…
Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…