606 research outputs found
Weyl group multiple Dirichlet series constructed from quadratic characters
We construct multiple Dirichlet series in several complex variables whose
coefficients involve quadratic residue symbols. The series are shown to have an
analytic continuation and satisfy a certain group of functional equations.
These are the first examples of an infinite collection of unstable Weyl group
multiple Dirichlet series in greater than two variables.Comment: incorporated referee's comment
Arithmetical properties of Multiple Ramanujan sums
In the present paper, we introduce a multiple Ramanujan sum for arithmetic
functions, which gives a multivariable extension of the generalized Ramanujan
sum studied by D. R. Anderson and T. M. Apostol. We then find fundamental
arithmetic properties of the multiple Ramanujan sum and study several types of
Dirichlet series involving the multiple Ramanujan sum. As an application, we
evaluate higher-dimensional determinants of higher-dimensional matrices, the
entries of which are given by values of the multiple Ramanujan sum.Comment: 19 page
Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
The Hall viscosity, a non-dissipative transport coefficient analogous to Hall
conductivity, is considered for quantum fluids in gapped or topological phases.
The relation to mean orbital spin per particle discovered in previous work by
one of us is elucidated with the help of examples, using the geometry of shear
transformations and rotations. For non-interacting particles in a magnetic
field, there are several ways to derive the result (even at non-zero
temperature), including standard linear response theory. Arguments for the
quantization, and the robustness of Hall viscosity to small changes in the
Hamiltonian that preserve rotational invariance, are given. Numerical
calculations of adiabatic transport are performed to check the predictions for
quantum Hall systems, with excellent agreement for trial states. The
coefficient of k^4 in the static structure factor is also considered, and shown
to be exactly related to the orbital spin and robust to perturbations in
rotation invariant systems also.Comment: v2: Now 30 pages, 10 figures; new calculation using disk geometry;
some other improvements; no change in result
Central limit theorem for multiplicative class functions on the symmetric group
Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for
the characteristic polynomial of a permutation matrix with respect to the
uniform measure on the symmetric group. We generalize this result in several
ways. We prove here a central limit theorem for multiplicative class functions
on symmetric group with respect to the Ewens measure and compute the covariance
of the real and the imaginary part in the limit. We also estimate the rate of
convergence with the Wasserstein distance.Comment: 23 pages; the mathematics is the same as in the previous version, but
there are several improvments in the presentation, including a more intuitve
name for the considered function
Berry Important? Wolf Provisions Pups with Berries in Northern Minnesota
Wolves (Canis lupus) primarily provision pups by catching mammalian prey and bringing remains of the carcass to the pups at a den or rendezvous site via their mouths or stomach. In August 2017, we observed an adult wolf regurgitating wild blueberries (Vaccinium spp.) to pups at a rendezvous site in the Greater Voyageurs Ecosystem, Minnesota, USA, which is the only known observation of wolves provisioning pups with wild berries. This observation, in combination with other evidence from the Greater Voyageurs Ecosystem, suggests wild berries might be a more valuable food source for wolves in southern boreal ecosystems than previously appreciated
Surgery for cystocele I—questions
Contains fulltext :
109642.pdf (publisher's version ) (Open Access
Haar expectations of ratios of random characteristic polynomials
We compute Haar ensemble averages of ratios of random characteristic
polynomials for the classical Lie groups K = O(N), SO(N), and USp(N). To that
end, we start from the Clifford-Weyl algebera in its canonical realization on
the complex of holomorphic differential forms for a C-vector space V. From it
we construct the Fock representation of an orthosymplectic Lie superalgebra osp
associated to V. Particular attention is paid to defining Howe's oscillator
semigroup and the representation that partially exponentiates the Lie algebra
representation of sp in osp. In the process, by pushing the semigroup
representation to its boundary and arguing by continuity, we provide a
construction of the Shale-Weil-Segal representation of the metaplectic group.
To deal with a product of n ratios of characteristic polynomials, we let V =
C^n \otimes C^N where C^N is equipped with its standard K-representation, and
focus on the subspace of K-equivariant forms. By Howe duality, this is a
highest-weight irreducible representation of the centralizer g of Lie(K) in
osp. We identify the K-Haar expectation of n ratios with the character of this
g-representation, which we show to be uniquely determined by analyticity, Weyl
group invariance, certain weight constraints and a system of differential
equations coming from the Laplace-Casimir invariants of g. We find an explicit
solution to the problem posed by all these conditions. In this way we prove
that the said Haar expectations are expressed by a Weyl-type character formula
for all integers N \ge 1. This completes earlier work by Conrey, Farmer, and
Zirnbauer for the case of U(N).Comment: LaTeX, 70 pages, Complex Analysis and its Synergies (2016) 2:
Vaginal Flora in Postmenopausal Women: The Effect of Estrogen Replacement
Objective:To determine the effect of estrogen replacement therapy (ERT)
on the vaginal flora of postmenopausal women
SL(2,Z) Multiplets in N=4 SYM Theory
We discuss the action of SL(2,Z) on local operators in D=4, N=4 SYM theory in
the superconformal phase. The modular property of the operator's scaling
dimension determines whether the operator transforms as a singlet, or
covariantly, as part of a finite or infinite dimensional multiplet under the
SL(2,Z) action. As an example, we argue that operators in the Konishi multiplet
transform as part of a (p,q) PSL(2,Z) multiplet. We also comment on the
non-perturbative local operators dual to the Konishi multiplet.Comment: 14 pages, harvmac; v2: published version with minor change
Twisted Frobenius-Schur indicators for Hopf algebras
The classical Frobenius-Schur indicators for finite groups are character sums
defined for any representation and any integer m greater or equal to 2. In the
familiar case m=2, the Frobenius-Schur indicator partitions the irreducible
representations over the complex numbers into real, complex, and quaternionic
representations. In recent years, several generalizations of these invariants
have been introduced. Bump and Ginzburg, building on earlier work of Mackey,
have defined versions of these indicators which are twisted by an automorphism
of the group. In another direction, Linchenko and Montgomery have defined
Frobenius-Schur indicators for semisimple Hopf algebras. In this paper, the
authors construct twisted Frobenius-Schur indicators for semisimple Hopf
algebras; these include all of the above indicators as special cases and have
similar properties.Comment: 12 pages. Minor revision
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