Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectrum Generating Conformal and Quasiconformal U-Duality Groups,
  Supergravity and Spherical Vectors   After reviewing the algebraic structures that underlie the geometries of N=2
Maxwell-Einstein supergravity theories (MESGT) in five and four dimensions with
symmetric scalar manifolds, we give a unified realization of their three
dimensional U-duality groups as spectrum generating quasiconformal groups. They
are F_{4(4)}, E_{6(2)}, E_{7(-5)}, E_{8(-24)} and SO(n+2,4). Our formulation is
covariant with respect to U-duality symmetry groups of corresponding five
dimensional supergravity theories, which are SL(3,R), SL(3,C), SU*(6), E_{6(6)}
and SO(n-1,1)X SO(1,1), respectively. We determine the spherical vectors of
quasiconformal realizations of all these groups twisted by a unitary character.
We also give their quadratic Casimir operators and determine their values. Our
work lays the algebraic groundwork for constructing the unitary representations
of these groups induced by their geometric quasiconformal actions, which
include the quaternionic discrete series. For rank 2 cases, SU(2,1) and
G_{2(2)}, corresponding to simple N=2 supergravity in four and five dimensions,
this program was carried out in arXiv:0707.1669. We also discuss the
corresponding algebraic structures underlying symmetries of matter coupled N=4
and N>4 supergravity theories. They lead to quasiconformal realizations of
split real forms of U-duality groups as a straightforward extension of the
quaternionic real forms.

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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph