Related papers: Spinors and forms on generalised cones
Two-sided Gaussian bounds are established for the weighted heat kernels on the unit ball and simplex in $\mathbb{R}^d$ generated by classical differential operators whose eigenfunctions are algebraic polynomials.
We develop the BPS preon conjecture to analyze the supersymmetric solutions of D=11 supergravity. By relating the notions of Killing spinors and BPS preons, we develop a moving G-frame method (G=GL(32,R), SL(32,R) or Sp(32,R)) to analyze…
We give a new expression for the inner product of two kernel functions associated to a cusp form. Among other applications, it yields an extension of a formula of Kohnen and Zagier, and another proof of Manin's Periods Theorem. Cohen's…
We determine the holonomy of generalized Killing spinor covariant derivatives of the form $D= \nabla + \Omega$ on pseudo-Riemannian reductive homogeneous spaces in a purely algebraic and algorithmic way, where $\Omega : TM \rightarrow…
The heat trace asymptotics on the noncommutative torus, where generalized Laplacians are made out of left and right regular representations, is fully determined. It turns out that this question is very sensitive to the number-theoretical…
In this paper, we fill some gap in the existing literature on higher spins by presenting an explicit solution to the on-shell constraints for a frame-like, gauge invariant description of massive, higher spin fields in d=4. We begin with the…
In this work we construct the heat kernel of the 1/2-order Laplacian perturbed by the first-order gradient term in H\"older space and the zero-order potential term in generalized Kato's class, and obtain sharp two-sided estimates as well as…
Jordan-Wigner-type transformations connecting the spin-3/2 operators and two kinds of fermions are derived. A general condition of fermionizability of spins is obtained and a theorem establishing connection between half integer spins and…
Spinorial methods have proven to be a powerful tool to study geometric properties of spin manifolds. Our aim is to continue the spinorial study of manifolds that are not necessarily spin. We introduce and study the notion of $G$-invariance…
In the superalgebraic representation of spinors using Grassmann densities and derivatives with respect to them, a generalization of Dirac conjugation is introduced, which provides Lorentz-covariant transformations of conjugate spinors. It…
We establish several refined strong multiplicity one results for paramodular cusp forms by using automorphic and Galois-theoretic methods. We also give an application to distinguishing eigenforms by the twisted central values of the spinor…
A representation of generalized Weierstrass formulae for an immersion of generic surfaces into a 4-dimensional complex space in terms of spinors treated as minimal left ideals of Clifford algebras is proposed. The relation between…
Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the…
In this paper we establish a formula for the average of representation numbers of ternary quadratic forms in a spinor genus over a totally real number field. The significant fact about the formula is the fact that it is given in terms of…
The higher spin Laplace operator has been constructed recently as the generalization of the Laplacian in higher spin theory. This acts on functions taking values in arbitrary irreducible representations of the Spin group. In this paper, we…
We investigate the combinatorics of the general formulas for the powers of the operator $h \partial^k$, where $h$ is a central element of a ring and $\partial$ is a differential operator. This generalizes previous work on the powers of…
We give explicit formulas for the intertwinors on the differential form bundles over $S^{p-1} \times S^{q-1}$ with the standard pseudo-Riemannian metric $g=-g_{{}_{S^{p-1}}}+g_{{}_{S^{q-1}}}$ of signature $(p-1,q-1)$. As a special case, we…
In this micro-canonical simulation the temperature and also the specific heat are determined as averages of expressions easy to implement. The XY-chain is studied for a test. The second order transition on a cubic lattice and the first…
We consider finite area convex Euclidean circular sectors. We prove a variational Polyakov formula which shows how the zeta-regularized determinant of the Laplacian varies with respect to the opening angle. Varying the angle corresponds to…
Matrix elements of spinor and principal series representations of the Lorentz group are studied in the basis of complex angular momentum (helicity basis). It is shown that matrix elements are expressed via hyperspherical functions…