The character of the principal series of representations of SL(n,R) is evaluated by using Gel’fand and Naimark’s definition of character. This representation is realized in the space of functions defined on the right coset space of SL(n,R) with respect to the subgroup of real triangular matrices. This form of the representations considerably simplifies the problem of determination of the integr...

We give tools to compare different maps from algebraic K-theory. The results apply in particular to group morphisms from K-theory to any suitable cohomology theory or to K-theory. In particular, we obtain a characterization of the Chern character and of the Adams operations on higher K-theory.

We introduce K-theoretic versions of the Fantechi-Goettsche ring of a variety with a group action and the Chen-Ruan cohomology of a smooth complex orbifold which we call stringy K-theory. Our definition is a generalization of a construction due to Givental and Y. P. Lee and it differs from the orbifold K-theory of Adem-Ruan. We also introduce a stringy Chern character isomorphism Ch taking stri...

The question raised by Shimony and Stein is examined and used to explain in more detail a key point of my proof that any theory that conforms to certain general ideas of orthodox relativistic quantum field theory must permit transfers of information over spacelike intervals. It is also explained why this result is not a problem for relativistic quantum theory, but, on the contrary, opens the do...

Brief introduction to cyclotomic theory over Q using adeles. Discussion of the definitions of modular forms and automorphic forms. Introducing the adelic automorphic forms via strong approximation theorem. Discussion of the connected components of Shimura varieties (modular curves). Smooth/admissible representations of locally finite groups. Definition and admissibility of (cuspidal) automorphi...

It was argued in [25], [5] that in the presence of a nontrivial Bfield, D-brane charges in type IIB string theories are classified by twisted Ktheory. In [4], it was proved that twisted K-theory is canonically isomorphic to bundle gerbe K-theory, whose elements are ordinary Hilbert bundles on a principal projective unitary bundle, with an action of the bundle gerbe determined by the principal p...

In this paper we consider a family of Dirac-type operators on fibration P → B equivariant with respect to an action of an étale groupoid. Such a family defines an element in the bivariant K theory. We compute the action of the bivariant Chern character of this element on the image of Connes’ map Φ in the cyclic cohomology. A particular case of this result is Connes’ index theorem for étale grou...

The representation theory of the symmetric groups Su aside from being extremely elegant and interesting in its own right can be used in a number of ways to obtain information about the representation theory of other classes of groups. This theory also turns out to have applications in such diverse areas of interest as atomic physics and quantum chemistry to graph isomorphism and PI algebras.