62 research outputs found
Uniqueness of Bessel models: the archimedean case
In the archimedean case, we prove uniqueness of Bessel models for general
linear groups, unitary groups and orthogonal groups.Comment: 22 page
A general form of Gelfand-Kazhdan criterion
We formalize the notion of matrix coefficients for distributional vectors in
a representation of a real reductive group, which consist of generalized
functions on the group. As an application, we state and prove a Gelfand-Kazhdan
criterion for a real reductive group in very general settings.Comment: 16 pages, to appear in Manuscripta Mathematic
Derivatives for smooth representations of GL(n,R) and GL(n,C)
The notion of derivatives for smooth representations of GL(n) in the p-adic
case was defined by J. Bernstein and A. Zelevinsky. In the archimedean case, an
analog of the highest derivative was defined for irreducible unitary
representations by S. Sahi and called the "adduced" representation. In this
paper we define derivatives of all order for smooth admissible Frechet
representations (of moderate growth). The archimedean case is more problematic
than the p-adic case; for example arbitrary derivatives need not be admissible.
However, the highest derivative continues being admissible, and for irreducible
unitarizable representations coincides with the space of smooth vectors of the
adduced representation. In [AGS] we prove exactness of the highest derivative
functor, and compute highest derivatives of all monomial representations.
We prove exactness of the highest derivative functor, and compute highest
derivatives of all monomial representations. We apply those results to finish
the computation of adduced representations for all irreducible unitary
representations and to prove uniqueness of degenerate Whittaker models for
unitary representations, thus completing the results of [Sah89, Sah90, SaSt90,
GS12].Comment: First version of this preprint was split into 2. The proofs of two
theorems which are technically involved in analytic difficulties were
separated into "Twisted homology for the mirabolic nilradical" preprint. All
the rest stayed in v2 of this preprint. v3: version to appear in the Israel
Journal of Mathematic
Curvature-coupling dependence of membrane protein diffusion coefficients
We consider the lateral diffusion of a protein interacting with the curvature
of the membrane. The interaction energy is minimized if the particle is at a
membrane position with a certain curvature that agrees with the spontaneous
curvature of the particle. We employ stochastic simulations that take into
account both the thermal fluctuations of the membrane and the diffusive
behavior of the particle. In this study we neglect the influence of the
particle on the membrane dynamics, thus the membrane dynamics agrees with that
of a freely fluctuating membrane. Overall, we find that this curvature-coupling
substantially enhances the diffusion coefficient. We compare the ratio of the
projected or measured diffusion coefficient and the free intramembrane
diffusion coefficient, which is a parameter of the simulations, with analytical
results that rely on several approximations. We find that the simulations
always lead to a somewhat smaller diffusion coefficient than our analytical
approach. A detailed study of the correlations of the forces acting on the
particle indicates that the diffusing inclusion tries to follow favorable
positions on the membrane, such that forces along the trajectory are on average
smaller than they would be for random particle positions.Comment: 16 pages, 8 figure
Autoequivalences of the category of schemes
We prove that there is no non-trivial autoequvivalence of the category of schemes of finite type over Q
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