Related papers: Dirac cohomology and character lifting
We show that the Dirac factorization method can be successfully employed to treat problems involving operators raised to a fractional power. The technique we adopt is based on an extension of the Pauli matrices and the properties of the…
The Dirac operator provides a unified framework for processing signals defined over different order topological domains, such as node and edge signals. Its eigenmodes define a spectral representation that inherently captures cross-domain…
An integer valued topological index of a Dirac operator is introduced for a pair of a 4n+2 dimensional open Spin^c manifold and a section of the determinant line bundle satisfying some property. We show a relation between the index and an…
We apply the concepts of superanalysis to present an intrinsically supersymmetric formulation of the Chern character in entire cyclic cohomology. We show that the cocycle condition is closely related to the invariance under…
We prove that the indices of fibered-cusp and $d$-Dirac operators on a spin manifold with fibered boundary coincide if the associated family of Dirac operators on the fibers of the boundary is invertible. This answers a question raised by…
In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac…
Dirac cohomology is a new tool to study unitary and admissible representations of semisimple Lie groups. It was introduced by Vogan and further studied by Kostant and ourselves \cite{V2}, \cite{HP1}, \cite{Kdircoh}. The aim of this paper is…
A signature independent formalism is created and utilized to determine the general second-order symmetry operators for Dirac's equation on two-dimensional Lorentzian spin manifolds. The formalism is used to characterize the orthonormal…
Let G be a compact, semi-simple Lie group and H a maximal rank reductive subgroup. The irreducible representations of G can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space G/H twisted…
We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class generalizing that of Killing spinors. We…
An integro-differential Dirac system with an integral term in the form of convolution is considered. We suppose that the convolution kernel is known a priori on a part of the interval, and recover it on the remaining part, using a part of…
We derive a Cooper-Frye type spin polarization formula for Dirac fermions at local thermal equilibrium described by a grand canonical ensemble specified by temperature, fluid velocity, chemical potential, and spin potential. We discuss the…
We exhibit a basis for the space of spherical characters of a distinguished supercuspidal representation $\pi$ of a connected reductive $p$-adic group, subject to the assumption that $\pi$ is obtained via induction from a representation of…
Exotic dark spinor fields are introduced and investigated in the context of inequivalent spin structures on arbitrary curved spacetimes, which induces an additional term on the associated Dirac operator, related to a Cech cohomology class.…
Molecular representations are of fundamental importance for the modeling and analysis of molecular systems. Representation models and in general approaches based on topological data analysis (TDA) have demonstrated great success in various…
We define analogues of the Casimir and Dirac operators for graded affine Hecke algebras, and establish a version of Parthasarathy's Dirac operator inequality. We then prove a version of Vogan's Conjecture for Dirac cohomology. The…
Following the quantisation of a graph with the Dirac operator (spin-1/2) we explain how additional weights in the spectral form factor K(\tau) due to spin propagation around orbits produce higher order terms in the small-\tau asymptotics in…
We consider modifications of the classical dbar-Neumann conditions that define Fredholm problems for the Spin_C Dirac operator. In part II, we use boundary layer methods to obtain subelliptic estimates for these boundary value problems.…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…
In this paper we will derive an explicit description of the genuine projective representations of the symmetric group $S_n$ using Dirac cohomology and the branching graph for the irreducible genuine projective representations of $S_n$. In…