Each symplectic group over the field of two elements has two exceptional doubly transitive actions on sets of quadratic forms on the defining symplectic vector space. This paper studies the associated 2-modular permutation modules. Filtrations of these modules are constructed which have subquotients which are modules for the symplectic group over an algebraically closed field of characteristic ...

For G real split, I studied the (non)-unitarity of a spherical principal series I(1, ν) of G by means of Weyl group representations. For a good choice of the parameter ν, the spherical principal series I(1, ν) admits an invariant hermitian form. To discuss the unitarity of I(1, ν), one needs to compute the signature of such a form. Computations can be done separately on the isotypic of each K−t...

We present a new way of obtaining the Bargmann transform between L 2 (R n) and the Fock space F = F(C n) via a simple restriction principle applied to holo-morphic functions. This same principle also recovers the transform between functions on a compact Lie group and holomorphic functions on its complexii-cation studied by Gross, Hall, Hijab et al., see 1] and 2], and it gives in a similar way ...

The Weyl double copy is a procedure for relating exact solutions in biadjoint scalar, gauge and gravity theories, relates fields spacetime directly. Where this comes from, how general it is, have until recently remained mysterious. In paper, we show the current form scope of can be derived from certain twistor space. new formalism shows that more than previously thought, applying particular to ...

863 news & views and patterning, opens up a wide range of new applications for hot-electron-driven chemistry. The LEE source might also prove a critical tool for obtaining a deeper nanoscale understanding of radiation chemistry and biology, and material degradation by high-energy radiation in general. The quantum description of spin-1/2 particles is given by the solutions of the Dirac equation....

We study the twisted Weyl symbol of metaplectic operators; this requires the definition of an index for symplectic paths related to the Conley–Zehnder index. We thereafter define a metaplectically covariant algebra of pseudo-differential operators acting on functions on symplectic space.