We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop like generators are found for the algebra which satisfy the relations of Drinfel ′ d's new realization. Coproduct formulas are given and a PBW type basis is constructed. §0. Introduction. The purpose of this pape...

g Z I Y ( t ) = exp (-nizy + 27r iy t ) g ( t z), t E w We truncate the channel response so that N , = 0 and AT, = 20. As before, the channel input is an i.i.d. sequence, and the noise is stationary and white with SNR,h,, =20 dB. We assume the number of feedforward taps is fixed at q = 10. Fig. 3 shows the optimal decision delay (defined as thlat which maximizes SNRDFE) versus the number of fee...

A Weyl-Heisenberg frame for L2(R) is a frame consisting of modulates Embg(t) = e 2πimbtg(t) and translates Tnag(t) = g(t − na), m,n ∈ Z, of a fixed function g ∈ L2(R), for a, b ∈ R. A fundamental question is to explicitly represent the families (g, a, b) so that (EmbTnag)m,n∈Z is a frame for L2(R). We will show an interesting connection between this question and a classical problem of Littlewoo...

We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the al...

We present a comprehensive analysis of the convergence properties of the frame operators of Weyl-Heisenberg systems and shift-invariant systems, and relate these to the convergence of the Walnut representation. We give a deep analysis of necessary conditions and sufficient conditions for convergence of the frame operator. We show that symmetric, norm and unconditional convergence of the Walnut ...

We address the issue of when generalized quantum dynamics, which is a classical symplectic dynamics for noncommuting operator phase space variables based on a graded total trace Hamiltonian H, reduces to Heisenberg picture complex quantum mechanics. We begin by showing that when H = TrH , with H a Weyl ordered operator Hamiltonian, then the generalized quantum dynamics operator equations of mot...

Cherednik attached to an affineHecke algebramodule a compatible systemof difference equations, called quantum affine Knizhnik–Zamolodchikov (KZ) equations. In the case of a principal series module, we construct a basis of power series solutions of the quantum affine KZ equations. Relating the bases for different asymptotic sectors gives rise to a Weyl group cocycle, which we compute explicitly ...

The Gottesman–Knill theorem established that stabilizer states and Clifford operations can be efficiently simulated classically. For qudits with odd dimension three and greater, stabilizer states and Clifford operations have been found to correspond to positive discrete Wigner functions and dynamics. We present a discrete Wigner function-based simulation algorithm for odd-d qudits that has the ...

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...