We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of [6, 4]. We prove this duality for the Kirillov–Reshetikhin modules. In the course of the proof we introduce and construct “interpolating (q, t)-characters” depending on two parameters which interpolate between the q-characte...

A result of Strunkov on generalised conjugacy classes of groups is most conveniently expressed in terms of the P-matrix of an association scheme. This result is dual to a result of Blichfeldt on permutation characters, which has been shown by Cameron and Kiyota to hold for arbitrary characters and led to the definition of sharp characters. We show that the result carries over to arbitrary (comm...

In previous work we derived the topological terms in the M-theory action in terms of certain characters that we defined. In this paper, we extend these characters to include the dual fields and to account for their dynamics. We start investigating the existence of a relation of this to various generalized cohomology theories by utilizing the Bott-like elements and forming homogeneous degree com...

In previous work we derived the topological terms in the M-theory action in terms of certain characters that we defined. In this paper, we propose the extention of these characters to include the dual fields. The unified treatment of the M-theory four-form field strength and its dual leads to several observations. In particular we elaborate on the possibility of a twisted cohomology theory with...

The notion of double coset for semisimple finite dimensional Hopf algebras is introduced. This is done by considering an equivalence relation on the set of irreducible characters of the dual Hopf algebra. As an application formulae for the restriction of the irreducible characters to normal Hopf subalgebras are given.

1 Euler Characteristics and Infinitesimal Characters 4 1.1 The unitary duals of SL2(R) and SL4(R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Euler characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Euler-Poincaré functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Euler characteristics in t...