Abstract The equivariant K -theory of the semi-infinite flag manifold, as developed recently by Kato, Naito, and Sagaki, carries commuting actions nil-double affine Hecke algebra (nil-DAHA) a q -Heisenberg algebra. action latter generates free submodule rank | W |, where is (finite) Weyl group. We show that this stable under nil-DAHA, which enables one to express nil-DAHA in terms $$|W|\times |...

in this paper, we obtain a necessary and sufficient condition for a conformal mapping between two weyl manifolds to preserve einstein tensor. then we prove that some basic curvature tensors of $w_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. also, we obtained the relation between the scalar curvatures of the weyl manifolds r...

An extensively tacit understandings of equivalency between the deformed HeisenbergWeyl algebra in noncommutative space and the undeformed Heisenberg-Weyl algebra in commutative space is elucidated. Equivalency conditions between two algebras are clarified. It is explored that the deformed algebra related to the undeformed one by a non-orthogonal similarity transformation. Furthermore, non-exist...

We study invertibility and compactness of positive Toeplitz operators associated to a continuous Parseval frame on Hilbert space. As applications, we characterize affine Weyl-Heisenberg localization as well give uncertainty principles for the transforms.

Abstract We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is fractional p -Laplacian operator on Heisenberg-Weyl group $$\mathbb {H}^n$$ H n </m...

Two complementary approaches ofN = 2 fractional supersymmetric quantum mechanics of order k are studied in this article. The first one, based on a generalized Weyl-Heisenberg algebra Wk (that comprizes the affine quantum algebra Uq(sl2) with q k = 1 as a special case), apparently contains solely one bosonic degree of freedom. The second one uses generalized bosonic and kfermionic degrees of fre...

Complex arrays with good aperiodic properties are characterised and it is shown how the joining of dimensions can generate sequences which retain the aperiodic properties of the parent array. For the case of 2× 2× . . .× 2 arrays we define two new notions of aperiodicity by exploiting a unitary matrix represention. In particular, we apply unitary rotations by members of a size-3 cyclic subgroup...

Abstract: Lüders’ theorem states that two observables commute if measuring one of them does not disturb the measurement outcomes of the other. We study measurements which are described by continuous positive operatorvalued measurements (or POVMs) associated with coherent states on a Lie group. In general, operators turn out to be invariant under the Lüders map if their P and Q-symbols coincide....

Within the algebraic framework of Hopf algebras, random walks and associated diffusion equations (master equations) are constructed and studied for two basic operator algebras of Quantum Mechanics i.e the Heisenberg-Weyl algebra (hw) and its q-deformed version hwq. This is done by means of functionals determined by the associated coherent state density operators. The ensuing master equations ad...

The Heisenberg double Dq(E2) of the quantum Euclidean group $${{\cal O}_q}({E_2})$$ is smash product with its Hopf dual $${U_q}({e_2})$$ . For algebra Dq(E2), explicit descriptions prime, primitive and maximal spectra are obtained. All prime factors presented as generalized Weyl algebras. As a result, we obtain that has no finite-dimensional representations, cannot have structure. automorphism ...