We classify all genuine unitary representations of the metaplectic group whose infinitesimal character is real and at least as regular as that of the oscillator representation. In a previous paper we exhibited a certain family of representations satisfying these conditions, obtained by cohomological induction from the tensor product of a one-dimensional representation and an oscillator represen...

Using a new definition of rank for representations of semisimple groups, sharp results are proved for the decay of matrix coefficients of unitary representations of two types of non-split p-adic simple algebraic groups of exceptional type. These sharp bounds are achieved by minimal representations. It is also shown that in one of the cases considered, the minimal representation is isolated in t...

We propose a definition of compact quantum groupoids in the setting of C -algebras, associate to such a quantum groupoid a regular C -pseudo-multiplicative unitary, and use this unitary to construct a dual Hopf C -bimodule and to pass to a measurable quantum groupoid in the sense of Enock and Lesieur. Moreover, we discuss examples related to compact and to étale groupoids and study principal co...

For each locally compact non-compact c-compact Abelian group G whose dual is an I-group and each compact Abelian group ,?J such that there is a one-to-one continous homomorphism from G onto a dense subgroup of Z, we show the existence of cocycles on Z whose associated unitary representations of G have purely singular continuous spectrum, as well as the existence of cocycles on Z whose associate...

Dual-unitary circuits are a class of locally interacting quantum many-body systems displaying unitary dynamics also when the roles space and time exchanged. These have recently emerged as remarkable framework where certain features chaos can be studied exactly. In particular, they admit ``solvable'' initial states for which, in thermodynamic limit, one access full nonequilibrium dynamics. This ...

Dual-unitary quantum circuits can be used to construct 1+1 dimensional lattice models for which dynamical correlations of local observables explicitly calculated. We show how analytically classes dual-unitary with any desired level (non-)ergodicity dimension the Hilbert space, and present analytical results thermalization an infinite-temperature Gibbs state (ergodic) a generalized ensemble (non...

While quantum circuits built from two-particle dual-unitary (maximally entangled) operators serve as minimal models of typically nonintegrable many-body systems, the construction and characterization themselves are only partially understood. A nonlinear map on space unitary was proposed in PRL.~125, 070501 (2020) that results being arbitrarily close to dual unitaries. Here we study analytically...