This paper gives the classification of the Whittaker unitary dual for affine graded Hecke algebras of type E. By the Iwahori-Matsumoto involution, this is equivalent also to the classification of the spherical unitary dual for type E. Together with [BM3], [Ba1] and [Ci1], this work completes the classification of the Whittaker Iwahori-spherical unitary dual, or equivalently, the spherical unita...

It is known that the determination of the Iwahori-spherical unitary dual for p-adic groups can be reduced to the classification of unitary representations with real infinitesimal character for the associated Hecke algebras. In this setting, I determine the Iwahori–spherical unitary dual for split

After quantum quenches in many-body systems, finite subsystems evolve nontrivially time, eventually approaching a stationary state. In typical situations, the reduced density matrix of given subsystem begins and ends this endeavor as low-entangled vector space operators. This means that if its entanglement operator initially grows (which is generically case), it must decrease, describing barrie...

Abstract Recently introduced dual unitary brickwork circuits have been recognised as paradigmatic exactly solvable quantum chaotic many-body systems with tunable degree of ergodicity and mixing. Here we show that regularity the circuit lattice is not crucial for exact solvability. We consider a where random 2-qubit gates sit at intersections arrangements straight lines in two dimensions ( mikad...

Over a non-archimedean local field of characteristic zero, we prove the multiplicity preservation for orthogonal-symplectic dual pair correspondences and unitary dual pair correspondences.

Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of ...

Circular Brownian motion models of random matrices were introduced by Dyson and describe the parametric eigenparameter correlations of unitary random matrices. For symmetric unitary, self-dual quaternion unitary and an analogue of antisymmetric hermitian matrix initial conditions, Brownian dynamics toward the unitary symmetry is analyzed. The dynamical correlation functions of arbitrary number ...

In this paper, we construct a splitting of the metaplectic cover of the reductive dual pairs of orthogonal and symplectic groups or the reductive dual pairs of unitary groups over a nonarchimedean local field with respect to a generalized lattice model of the Weil representation. We also prove a result concerning the splitting that we construct and the theta dichotomy for unitary group. The spl...