Let G be a compact Lie group with H and K arbitrary closed subgroups. Let BG, BH, BK be /-universal classifying spaces, with p{H, G): BH -» BG the natural projection. Then transfer homomorphisms J\H, G): h(BH) -» h(BG) are defined for h an arbitrary cohomology theory. One of the basic properties of the transfer for finite coverings is a double coset formula. This paper proves a double coset the...

The concept of the ‘Wigner rotation’, familiar from the composition law of (pure) Lorentz transformations, is described in the general setting of Lie group coset spaces and the properties of coset representatives. Examples of Abelian and non-Abelian Wigner rotations are given. The Lorentz group Wigner rotation, occurring in the coset space SL(2, R)/SO(2) SO(2, 1)/SO(2), is shown to be an analyt...

We study a coset-space unification model for families based on E 7 /SU(5)×U(1) 3. We find that qualitative structure of quark and lep-ton mass matrices in this model describes very well the observation. We stress, in particular, that the large mixing angle, sin 2 2θ νµντ ≃ 1, required for the atmospheric neutrino oscillation reported by the Su-perKamiokande collaboration, is naturally obtained,...

We review the recently discovered connection between the Belinsky-Khalatnikov-Lifshitz-like “chaotic” structure of generic cosmological singularities in eleven-dimensional supergravity and the “last” hyperbolic Kac-Moody algebra E10. This intriguing connection suggests the existence of a hidden “correspondence” between supergravity (or even M-theory) and null geodesic motion on the infinite-dim...

Let G denote a connected reductive group over a nonarchimedean local field F . Let K denote a special maximal parahoric subgroup of G(F ). We establish a Satake isomorphism for the Hecke algebra HK of K-bi-invariant compactly supported functions on G(F ). The key ingredient is a Cartan decomposition describing the double coset space K\G(F )/K. We also describe how our results relate to the trea...