1,933 research outputs found
Spectral transfer morphisms for unipotent affine Hecke algebras
In this paper we will give a complete classification of the spectral transfer
morphisms between the unipotent affine Hecke algebras of the various inner
forms of a given quasi-split absolutely simple algebraic group, defined over a
non-archimidean local field and split over an unramified extension
of . As an application of these results, the results of [O4] on the
spectral correspondences associated with such morphisms and some results of
Ciubotaru, Kato and Kato [CKK] we prove a conjecture of Hiraga, Ichino and
Ikeda [HII] on the formal degrees and adjoint gamma factors for all unipotent
discrete series characters of unramified simple groups of adjoint type defined
over .Comment: 61 pages; We explained the comparison with Lusztig's parameterization
of unipotent representations in more detai
To be or not to be? Magnetic monopoles in non-abelian gauge theories
Magnetic monopoles form an inspiring chapter of theoretical physics, covering
a variety of surprising subjects. We review their role in non-abelian gauge
theories. An expose of quite exquisite physics derived from a hypothetical
particle species, because the fact remains that in spite of ever more tempting
arguments from theory, monopoles have never reared their head in experiment.
For many relevant particulars, references to the original literature are
provided.Comment: 34 pages, 7 figures, Contribution to "Fifty Years of Yang- Mills
Theory", edited by G. 't Hooft. Some extra references have been added in the
revised versio
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Topological dualities in the Ising model
We relate two classical dualities in low-dimensional quantum field theory:
Kramers-Wannier duality of the Ising and related lattice models in
dimensions, with electromagnetic duality for finite gauge theories in
dimensions. The relation is mediated by the notion of boundary field theory:
Ising models are boundary theories for pure gauge theory in one dimension
higher. Thus the Ising order/disorder operators are endpoints of Wilson/'t
Hooft defects of gauge theory. Symmetry breaking on low-energy states reflects
the multiplicity of topological boundary states. In the process we describe
lattice theories as (extended) topological field theories with boundaries and
domain walls. This allows us to generalize the duality to non-abelian groups;
finite, semi-simple Hopf algebras; and, in a different direction, to finite
homotopy theories in arbitrary dimension
Four dimensional Abelian duality and SL(2,Z) action in three dimensional conformal field theory
Recently, Witten showed that there is a natural action of the group SL(2,Z)
on the space of 3 dimensional conformal field theories with U(1) global
symmetry and a chosen coupling of the symmetry current to a background gauge
field on a 3-fold N. He further argued that, for a class of conformal field
theories, in the nearly Gaussian limit, this SL(2,Z) action may be viewed as a
holographic image of the well-known SL(2,Z) Abelian duality of a pure U(1)
gauge theory on AdS-like 4-folds M bounded by N, as dictated by the AdS/CFT
correspondence. However, he showed that explicitly only for the generator T;
for the generator S, instead, his analysis remained conjectural. In this paper,
we propose a solution of this problem. We derive a general holographic formula
for the nearly Gaussian generating functional of the correlators of the
symmetry current and, using this, we show that Witten's conjecture is indeed
correct when N=S^3. We further identify a class of homology 3-spheres N for
which Witten's conjecture takes a particular simple form.Comment: analysis of sect. 5 generalized; 43 pages, Plain TeX, no figures,
requires AMS font files amssym.def and amssym.te
The Langlands-Kottwitz approach for some simple Shimura Varieties
We show how the Langlands-Kottwitz method can be used to determine the
semisimple local factors of the Hasse-Weil zeta-function of certain Shimura
varieties. On the way, we prove a conjecture of Haines and Kottwitz in this
special case.Comment: 23 page
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