794 research outputs found
Hecke algebras of finite type are cellular
Let \cH be the one-parameter Hecke algebra associated to a finite Weyl
group , defined over a ground ring in which ``bad'' primes for are
invertible. Using deep properties of the Kazhdan--Lusztig basis of \cH and
Lusztig's \ba-function, we show that \cH has a natural cellular structure
in the sense of Graham and Lehrer. Thus, we obtain a general theory of ``Specht
modules'' for Hecke algebras of finite type. Previously, a general cellular
structure was only known to exist in types and .Comment: 14 pages; added reference
Generalized Farey trees, transfer Operators and phase transitions
We consider a family of Markov maps on the unit interval, interpolating
between the tent map and the Farey map. The latter map is not uniformly
expanding. Each map being composed of two fractional linear transformations,
the family generalizes many particular properties which for the case of the
Farey map have been successfully exploited in number theory. We analyze the
dynamics through the spectral analysis of generalized transfer operators.
Application of the thermodynamic formalism to the family reveals first and
second order phase transitions and unusual properties like positivity of the
interaction function.Comment: 39 pages, 10 figure
On the Representation Theory of an Algebra of Braids and Ties
We consider the algebra introduced by F. Aicardi and J.
Juyumaya as an abstraction of the Yokonuma-Hecke algebra. We construct a tensor
space representation for and show that this is faithful. We use
it to give a basis for and to classify its irreducible
representations.Comment: 24 pages. Final version. To appear in Journal of Algebraic
Combinatorics
Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order
We employ computer algebra algorithms to prove a collection of identities
involving Bessel functions with half-integer orders and other special
functions. These identities appear in the famous Handbook of Mathematical
Functions, as well as in its successor, the DLMF, but their proofs were lost.
We use generating functions and symbolic summation techniques to produce new
proofs for them.Comment: Final version, some typos were corrected. 21 pages, uses svmult.cl
Recommended from our members
Flexible human machine interface for process diagnostics
A flexible human machine interface to design and display graphical and textual process diagnostic information is presented. The system operates on different computer hardware platforms, including PCs under MS Windows and UNIX Workstations under X-Windows, in a client-server architecture. The interface system is customized for specific process applications in a graphical user interface development environment by overlaying the image of the process piping and instrumentation diagram with display objects that are highlighted in color during diagnostic display. Customization of the system is presented for Commonwealth Edison`s Braidwood PWR Chemical and Volume Control System with transients simulated by a full-scale operator-training simulator and diagnosed by a computer-based system
Draft genome sequence of isolate Staphylococcus aureus LHSKBClinical, isolated from an infected hip
We report here the genome sequence of a clinical isolate of <i>Staphylococcus aureus</i> from an orthopedic infection. Phenotypically diverse <i>Staphylococcus aureus</i> strains are associated with orthopedic infections and subsequent implant failure, and some are highly resistant to antibiotics. This genome sequence will support further analyses of strains causing orthopedic infections
Partition functions and double-trace deformations in AdS/CFT
We study the effect of a relevant double-trace deformation on the partition
function (and conformal anomaly) of a CFT at large N and its dual picture in
AdS. Three complementary previous results are brought into full agreement with
each other: bulk and boundary computations, as well as their formal identity.
We show the exact equality between the dimensionally regularized partition
functions or, equivalently, fluctuational determinants involved. A series of
results then follows: (i) equality between the renormalized partition functions
for all d; (ii) for all even d, correction to the conformal anomaly; (iii) for
even d, the mapping entails a mixing of UV and IR effects on the same side
(bulk) of the duality, with no precedent in the leading order computations; and
finally, (iv) a subtle relation between overall coefficients, volume
renormalization and IR-UV connection. All in all, we get a clean test of the
AdS/CFT correspondence beyond the classical SUGRA approximation in the bulk and
at subleading O(1) order in the large-N expansion on the boundary.Comment: 18 pages, uses JHEP3.cls. Published JHEP versio
Azimuthal correlation in DIS
We introduce the azimuthal correlation for the deep inelastic scattering
process. We present the QCD prediction to the level of next-to-leading log
resummation, matching to the fixed order prediction. We also estimate the
leading non-perturbative power correction. The observable is compared with the
energy-energy correlation in e+e- annihilation, on which it is modelled. The
effects of the resummation and of the leading power correction are both quite
large. It would therefore be particularly instructive to study this observable
experimentally.Comment: 33 pages, 4 figures, JHEP class included. One figure and some
clarifications adde
On the validity of entropy production principles for linear electrical circuits
We discuss the validity of close-to-equilibrium entropy production principles
in the context of linear electrical circuits. Both the minimum and the maximum
entropy production principle are understood within dynamical fluctuation
theory. The starting point are Langevin equations obtained by combining
Kirchoff's laws with a Johnson-Nyquist noise at each dissipative element in the
circuit. The main observation is that the fluctuation functional for time
averages, that can be read off from the path-space action, is in first order
around equilibrium given by an entropy production rate. That allows to
understand beyond the schemes of irreversible thermodynamics (1) the validity
of the least dissipation, the minimum entropy production, and the maximum
entropy production principles close to equilibrium; (2) the role of the
observables' parity under time-reversal and, in particular, the origin of
Landauer's counterexample (1975) from the fact that the fluctuating observable
there is odd under time-reversal; (3) the critical remark of Jaynes (1980)
concerning the apparent inappropriateness of entropy production principles in
temperature-inhomogeneous circuits.Comment: 19 pages, 1 fi
Boundary Liouville theory at c=1
The c=1 Liouville theory has received some attention recently as the
Euclidean version of an exact rolling tachyon background. In an earlier paper
it was shown that the bulk theory can be identified with the interacting c=1
limit of unitary minimal models. Here we extend the analysis of the c=1-limit
to the boundary problem. Most importantly, we show that the FZZT branes of
Liouville theory give rise to a new 1-parameter family of boundary theories at
c=1. These models share many features with the boundary Sine-Gordon theory, in
particular they possess an open string spectrum with band-gaps of finite width.
We propose explicit formulas for the boundary 2-point function and for the
bulk-boundary operator product expansion in the c=1 boundary Liouville model.
As a by-product of our analysis we also provide a nice geometric interpretation
for ZZ branes and their relation with FZZT branes in the c=1 theory.Comment: 37 pages, 1 figure. Minor error corrected, slight change in result
(1.6
- …