1,196 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
Polarizations and Nullcone of Representations of Reductive Groups
The paper starts with the following simple observation. Let V be a representation of a reductive group G, and let f_1,f_2,...,f_n be homogeneous invariant functions. Then the polarizations of f_1,f_2,...,f_n define the nullcone of k 0} h(t) x = 0 for all x in L. This is then applied to many examples. A surprising result is about the group SL(2,C) where almost all representations V have the property that all linear subspaces of the nullcone are annihilated. Again, this has interesting applications to the invariants on several copies. Another result concerns the n-qubits which appear in quantum computing. This is the representation of a product of n copies of on the n-fold tensor product C^2 otimes C^2 otimes ... otimes C^2. Here we show just the opposite, namely that the polarizations never define the nullcone of several copies if n <= 3. (An earlier version of this paper, distributed in 2002, was split into two parts; the first part with the title ``On the nullcone of representations of reductive groups'' is published in Pacific J. Math. {bf 224} (2006), 119--140.
BPS black holes, quantum attractor flows and automorphic forms
We propose a program for counting microstates of four-dimensional BPS black
holes in N >= 2 supergravities with symmetric-space valued scalars by
exploiting the symmetries of timelike reduction to three dimensions. Inspired
by the equivalence between the four dimensional attractor flow and geodesic
flow on the three-dimensional scalar manifold, we radially quantize stationary,
spherically symmetric BPS geometries. Connections between the topological
string amplitude, attractor wave function, the Ooguri-Strominger-Vafa
conjecture and the theory of automorphic forms suggest that black hole
degeneracies are counted by Fourier coefficients of modular forms for the
three-dimensional U-duality group, associated to special "unipotent"
representations which appear in the supersymmetric Hilbert space of the quantum
attractor flow.Comment: 9 pages, revtex; v2: references added and typos correcte
A critical test of the assumption that men prefer conformist women and women prefer nonconformist men.
Five studies tested the common assumption that women prefer nonconformist men as romantic partners, whereas men prefer conformist women. Studies 1 and 2 showed that both men and women preferred nonconformist romantic partners, but women overestimated the extent to which men prefer conformist partners. In Study 3, participants ostensibly in a small-group interaction showed preferences for nonconformist opposite-sex targets, a pattern that was particularly evident when men evaluated women. Dating success was greater the more nonconformist the sample was (Study 4), and perceptions of nonconformity in an ex-partner were associated with greater love and attraction toward that partner (Study 5). On the minority of occasions in which effects were moderated by gender, it was in the reverse direction to the traditional wisdom: Conformity was more associated with dating success among men. The studies contradict the notion that men disproportionately prefer conformist women
System of Complex Brownian Motions Associated with the O'Connell Process
The O'Connell process is a softened version (a geometric lifting with a
parameter ) of the noncolliding Brownian motion such that neighboring
particles can change the order of positions in one dimension within the
characteristic length . This process is not determinantal. Under a special
entrance law, however, Borodin and Corwin gave a Fredholm determinant
expression for the expectation of an observable, which is a softening of an
indicator of a particle position. We rewrite their integral kernel to a form
similar to the correlation kernels of determinantal processes and show, if the
number of particles is , the rank of the matrix of the Fredholm determinant
is . Then we give a representation for the quantity by using an -particle
system of complex Brownian motions (CBMs). The complex function, which gives
the determinantal expression to the weight of CBM paths, is not entire, but in
the combinatorial limit it becomes an entire function providing
conformal martingales and the CBM representation for the noncolliding Brownian
motion is recovered.Comment: v3: AMS_LaTeX, 25 pages, no figure, minor corrections made for
publication in J. Stat. Phy
Statistical Mechanics of Membrane Protein Conformation: A Homopolymer Model
The conformation and the phase diagram of a membrane protein are investigated
via grand canonical ensemble approach using a homopolymer model. We discuss the
nature and pathway of -helix integration into the membrane that results
depending upon membrane permeability and polymer adsorptivity. For a membrane
with the permeability larger than a critical value, the integration becomes the
second order transition that occurs at the same temperature as that of the
adsorption transition. For a nonadsorbing membrane, the integration is of the
first order due to the aggregation of -helices.Comment: RevTeX with 5 postscript figure
The resource theory of quantum reference frames: manipulations and monotones
Every restriction on quantum operations defines a resource theory,
determining how quantum states that cannot be prepared under the restriction
may be manipulated and used to circumvent the restriction. A superselection
rule is a restriction that arises through the lack of a classical reference
frame and the states that circumvent it (the resource) are quantum reference
frames. We consider the resource theories that arise from three types of
superselection rule, associated respectively with lacking: (i) a phase
reference, (ii) a frame for chirality, and (iii) a frame for spatial
orientation. Focussing on pure unipartite quantum states (and in some cases
restricting our attention even further to subsets of these), we explore
single-copy and asymptotic manipulations. In particular, we identify the
necessary and sufficient conditions for a deterministic transformation between
two resource states to be possible and, when these conditions are not met, the
maximum probability with which the transformation can be achieved. We also
determine when a particular transformation can be achieved reversibly in the
limit of arbitrarily many copies and find the maximum rate of conversion. A
comparison of the three resource theories demonstrates that the extent to which
resources can be interconverted decreases as the strength of the restriction
increases. Along the way, we introduce several measures of frameness and prove
that these are monotonically nonincreasing under various classes of operations
that are permitted by the superselection rule.Comment: 37 pages, 4 figures, Published Versio
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