Abstract We classify Harish-Chandra modules generated by the pullback to metaplectic group of harmonic weak Maaß forms with exponential growth allowed at cusps. This extends work Schulze-Pillot and parallels recent Bringmann–Kudla, who investigated case integral weights. realize each our cases via a regularized theta lift an weight form. in both half-integral that occur need not be irreducible....

Abstract The Weyl–Wigner representations for canonical thermal equilibrium quantum states are obtained the whole class of quadratic Hamiltonians through a Wick rotation symbols Heisenberg and metaplectic operators. behavior classical structures inherently associated to these unitaries is described under mapping, unveiling that state fully determined by complex symplectic matrix, which sets all ...

Abstract Lapid and Mao formulated a conjecture on an explicit formula of Whittaker–Fourier coefficients automorphic forms quasi-split reductive groups metaplectic as analogue the Ichino–Ikeda conjecture. They also showed that this is reduced to certain local identity in case unitary groups. In article, we study even unitary-group case. Indeed, prove over p -adic fields. Further, equivalence bet...

Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrable representations of the shearlet groups provide not only the basis for the shearlet transforms but also for a very natural definition of scales of smoothness spaces, called shearlet coorbit spaces. The aim of this pa...