Related papers: A pseudo-differential calculus on the Heisenberg g…
In this paper, we show that the semiclassical calculus recently developed on nilpotent Lie groups and nilmanifolds include the functional calculus of suitable subelliptic operators. Moreover, we obtain Weyl laws for these operators. Amongst…
A non-commutative differential calculus on the $h$-superplane is presented via a contraction of the $q$-superplane. An R-matrix which satisfies both ungraded and graded Yang-Baxter equations is obtained and a new deformation of the $(1+1)$…
In this paper we obtain a Liouville type theorem to the semilinear subcritical elliptic equation on H-type groups. The semilinear subcritical elliptic equation studied in this paper is a generalization of a classical semilinear subcritical…
The coinvariant algebra of a Weyl group plays a fundamental role in several areas of mathematics. The fake degrees are the graded multiplicities of the irreducible modules of a Weyl group in its coinvariant algebra, and they were computed…
In this expository paper we present an overview of various graphical categorifications of the Heisenberg algebra and its Fock space representation. We begin with a discussion of "weak" categorifications via modules for Hecke algebras and…
Let $G$ be an arbitrary compact Lie group. In this work we apply the method of the analytic continuation of traces in order to compute the Wodzicki residue for a classical pseudo-differential operator on $G$ in terms of its matrix-valued…
We categorify a quantized Heisenberg algebra associated to a finite subgroup of SL(2,C).
Given a Hopf algebra $A$ graded by a discrete group together with an action of the same group preserving the grading, we define a new Hopf algebra, which we call the graded twisting of $A$. If the action is adjoint, this new Hopf algebra is…
In the spirit of geometric quantisation we consider representations of the Heisenberg(--Weyl) group induced by hypercomplex characters of its centre. This allows to gather under the same framework, called p-mechanics, the three principal…
A new pseudoclassical model to describe Weyl particles is proposed. Different ways of its quantization are presented. They all lead to the theory of Weyl particle; namely, the massless Dirac equation and the Weyl condition are reproduced.…
Given a compact manifold $M$ with boundary $\partial M$, in this paper we introduce a global symbolic calculus of pseudo-differential operators associated to $(M,\partial M)$. The symbols of operators with boundary conditions on $\partial…
In this article, we study two different types of operators, the localization operator and Weyl transform, on the reduced Heisenberg group with multidimensional center $\mathcal{G}$. The group $\mathcal{G}$ is a quotient group of…
Classical pseudo-differential operators of order zero on a graded nilpotent Lie group $G$ form a $^*$-subalgebra of the bounded operators on $L^2(G)$. We show that its $C^*$-closure is an extension of a noncommutative algebra of principal…
We prove a sharp Weyl estimate for the number of eigenvalues belonging to a fixed interval of energy of a self-adjoint difference operator acting on $\ell^2(\epsilon\mathbb{Z}^d)$ if the associated symplectic volume of phase space in…
We study the Nichols algebra of a semisimple Yetter-Drinfeld module and introduce new invariants such as real roots. The crucial ingredient is a `reflection' in the class of such Nichols algebras. We conclude the classifications of…
In this paper a bisingular pseudodifferential calculus, along the lines of the one introduced by L. Rodino in [12], is developed in the global setting of a product of compact Lie groups. The approach follows that introduced by M. Ruzhansky…
In this work we obtain continuity results on H\"older spaces for operators belonging to a Weyl-H\"ormander calculus for metrics such that the class of the associated operators contains, in particular, certain hypoelliptic laplacians. With…
In this work, we introduce a global theory of subelliptic pseudo-differential operators on arbitrary homogeneous vector bundles over orientable compact homogeneous manifolds. We will show that a global pseudo-differential calculus can be…
On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour. In the…
We give definition of a holonomy flag in subRiemannian geometry --- a generalization of a Riemannian holonomy algebra --- and calculate it for the 3D subRiemannian Lie groups. We rewrite and give new interpretation for the Codazzi equations…