518 research outputs found

### Quantum Cosmology and Conformal Invariance

According to Belinsky, Khalatnikov and Lifshitz, gravity near a space-like
singularity reduces to a set of decoupled one-dimensional mechanical models at
each point in space. We point out that these models fall into a class of
conformal mechanical models first introduced by de Alfaro, Fubini and Furlan
(DFF). The deformation used by DFF to render the spectrum discrete corresponds
to a negative cosmological constant. The wave function of the universe is the
zero-energy eigenmode of the Hamiltonian, also known as the spherical vector of
the representation of the conformal group SO(1,2). A new class of conformal
quantum mechanical models is constructed, based on the quantization of
nilpotent coadjoint orbits, where the conformal group is enhanced to an ADE
non-compact group for which the spherical vector is known.Comment: 4 pages, latex2e, uses revtex

### Minimal representations, spherical vectors, and exceptional theta series I

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 Schr\"odinger representation of symplectic groups. The real spherical vector invariant under the maximal compact subgroup is computed in this representation and yields the action appearing in the summand of the automorphic theta series. The summation measure can be obtained from the p-adic form of the spherical vector and is left to the sequel of this paper. The simplicity of our result is suggestive of a new Born-Infeld-like description of the membrane where U-duality is realized non-linearly. Our results may also be used in constructing quantum mechanical systems with hidden non-compact symmetries

### A logarithmic generalization of tensor product theory for modules for a vertex operator algebra

We describe a logarithmic tensor product theory for certain module categories
for a ``conformal vertex algebra.'' In this theory, which is a natural,
although intricate, generalization of earlier work of Huang and Lepowsky, we do
not require the module categories to be semisimple, and we accommodate modules
with generalized weight spaces. The corresponding intertwining operators
contain logarithms of the variables.Comment: 39 pages. Misprints corrected. Final versio

### The Impact of Non-Equipartition on Cosmological Parameter Estimation from Sunyaev-Zel'dovich Surveys

The collisionless accretion shock at the outer boundary of a galaxy cluster
should primarily heat the ions instead of electrons since they carry most of
the kinetic energy of the infalling gas. Near the accretion shock, the density
of the intracluster medium is very low and the Coulomb collisional timescale is
longer than the accretion timescale. Electrons and ions may not achieve
equipartition in these regions. Numerical simulations have shown that the
Sunyaev-Zel'dovich observables (e.g., the integrated Comptonization parameter
Y) for relaxed clusters can be biased by a few percent. The Y-mass relation can
be biased if non-equipartition effects are not properly taken into account.
Using a set of hydrodynamical simulations, we have calculated three potential
systematic biases in the Y-mass relations introduced by non-equipartition
effects during the cross-calibration or self-calibration when using the galaxy
cluster abundance technique to constraint cosmological parameters. We then use
a semi-analytic technique to estimate the non-equipartition effects on the
distribution functions of Y (Y functions) determined from the extended
Press-Schechter theory. Depending on the calibration method, we find that
non-equipartition effects can induce systematic biases on the Y functions, and
the values of the cosmological parameters Omega_8, sigma_8, and the dark energy
equation of state parameter w can be biased by a few percent. In particular,
non-equipartition effects can introduce an apparent evolution in w of a few
percent in all of the systematic cases we considered. Techniques are suggested
to take into account the non-equipartition effect empirically when using the
cluster abundance technique to study precision cosmology. We conclude that
systematic uncertainties in the Y-mass relation of even a few percent can
introduce a comparable level of biases in cosmological parameter measurements.Comment: 10 pages, 3 figures, accepted for publication in the Astrophysical
Journal, abstract abridged slightly. Typos corrected in version

### On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups

In this paper, we consider the relation between two nonabelian Fourier
transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig
parameters for unipotent elliptic representations of a split p-adic group and
the second is defined in terms of the pseudocoefficients of these
representations and Lusztig's nonabelian Fourier transform for characters of
finite groups of Lie type. We exemplify this relation in the case of the p-adic
group of type G_2.Comment: 17 pages; v2: several minor corrections, references added; v3:
corrections in the table with unipotent discrete series of G

### A unified approach on Springer fibers in the hook, two-row and two-column cases

We consider the Springer fiber over a nilpotent endomorphism. Fix a Jordan
basis and consider the standard torus relative to this. We deal with the
problem to describe the flags fixed by the torus which belong to a given
component of the Springer fiber. We solve the problem in the hook, two-row and
two-column cases. We provide two main characterizations which are common to the
three cases, and which involve dominance relations between Young diagrams and
combinatorial algorithms. Then, for these three cases, we deduce topological
properties of the components and their intersections.Comment: 42 page

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