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We introduce a categorical framework for the study of representations of G F , where G is a reductive group, and F is a 2-dimensional local field, i.e. F = K((t)), where K is a local field. Our main result says that the space of functions on G F , which is an object of a suitable category of representations of G F with the respect to the action of G on(More)
This paper is a continuation of [EK1-4]. The goal of this paper is to define and study the notion of a quantum vertex operator algebra (VOA) in the setting of the formal deformation theory and give interesting examples of such algebras. Our definition of a quantum VOA is based on the ideas of the paper [FrR]. The first chapter of our paper is devoted to the(More)
By Langlands duality one usually understands a correspondence between automor-phic representations of a reductive group G over the ring of adels of a field F , and homomorphisms from the Galois group Gal(F /F) to the Langlands dual group G L. It was originally introduced in the case when F is a number field or the field of rational functions on a curve over(More)
It is widely believed that many planar lattice models at the critical temperature are conformally invariant in the scaling limit. In particular, the Ising model is often cited as a classical example of conformal invariance which is used in deriving many of its properties. To the best of our knowledge no mathematical proof of this assertion has ever been(More)
In the paper [Dr3] V.Drinfeld formulated a number of problems in quantum group theory. In particular, he raised the question about the existence of a universal quantization for Lie bialgebras, which arose from the problem of quantization of Poisson Lie groups. When the paper [KL] appeared Drinfeld asked whether the methods of [KL] could be useful for the(More)
We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of Denef,Loeser, Cluckers. The method depends on an analysis of definable sets up to definable bijections. We obtain a(More)
Theta series for exceptional groups have been suggested as a possible description of the eleven-dimensional quantized BPS membrane. We present explicit formulae for these automorphic forms whenever the underlying Lie group G is simply laced. Specifically, we review and construct explicitly the minimal representation of G which generalizes the Schrödinger(More)
In the first part of this paper we study minimal representations of simply connected simple split groups G of type D k or E k over local non-archimedian fields. Our main result is an explicit formula for the spherical vectors in these representations. In the case of groups over R and C, such a formula was obtained recently in [8]. We also use our techniques(More)