227 research outputs found
Drinfeld second realization of the quantum affine superalgebras of via the Weyl groupoid
We obtain Drinfeld second realization of the quantum affine superalgebras
associated with the affine Lie superalgebra . Our results are
analogous to those obtained by Beck for the quantum affine algebras. Beck's
analysis uses heavily the (extended) affine Weyl groups of the affine Lie
algebras. In our approach the structures are based on a Weyl groupoid.Comment: 40 pages, 1 figure. close to the final version to appear in RIMS
Kokyuroku Bessatsu (Besstsu) B8 (2008) 171-21
The annual rate of independent events - A key interpretation for traditional extreme value distributions of wind velocity
The extreme value theory has been object of engineering studies for more than a century. The analysis of extreme winds plays a key role for complex civil structures and a driving role in different stages of wind turbines lifetime. Most of extremes probability models depend on the annual rate of independent events (ARIE) which has been traditionally considered a constant value. The authors have embraced a recent belief considering the ARIE as a function of the wind velocity. Even though a certain agreement has been achieved across the researches, some issues are still pending. In this regard, the paper shows that the annual, seasonal and daily fluctuations embedded in time series of the mean wind speeds, constrain its probability distribution and time correlation to be physically consistent. Besides, a new physical interpretation of the ARIE is presented, expressing how the independence across wind observations increases with the wind speed, up to the point that all yearly observations are independent if larger than a suitable speed value. Such a tendency is not revealed if the annual, seasonal and daily fluctuations are excluded by the analysis, leading to a deceitful shape of the ARIE. Finally, the paper shows how the velocity-dependent ARIE model is consistent with the conventional asymptotic extreme value theory, if a sufficiently large left-censorship applies to the dataset. The study of the ARIE presented in this paper is based on long-term Monte Carlo simulation of the mean wind speed
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Large N expansion of q-deformed two-dimensional Yang-Mills theory and hecke algebras
We derive the q-deformation of the chiral Gross-Taylor holomorphic string
large N expansion of two dimensional SU(N) Yang-Mills theory. Delta functions
on symmetric group algebras are replaced by the corresponding objects
(canonical trace functions) for Hecke algebras. The role of the Schur-Weyl
duality between unitary groups and symmetric groups is now played by q-deformed
Schur-Weyl duality of quantum groups. The appearance of Euler characters of
configuration spaces of Riemann surfaces in the expansion persists. We discuss
the geometrical meaning of these formulae
Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory
The classical analysis of Kazakov and Kostov of the Makeenko-Migdal loop
equation in two-dimensional gauge theory leads to usual partial differential
equations with respect to the areas of windows formed by the loop. We extend
this treatment to the case of U(N) Yang-Mills defined on the noncommutative
plane. We deal with all the subtleties which arise in their two-dimensional
geometric procedure, using where needed results from the perturbative
computations of the noncommutative Wilson loop available in the literature. The
open Wilson line contribution present in the non-commutative version of the
loop equation drops out in the resulting usual differential equations. These
equations for all N have the same form as in the commutative case for N to
infinity. However, the additional supplementary input from factorization
properties allowing to solve the equations in the commutative case is no longer
valid.Comment: 20 pages, 3 figures, references added, small clarifications adde
On the Hopf algebra structure of the AdS/CFT S-matrix
We formulate the Hopf algebra underlying the su(2|2) worldsheet S-matrix of
the AdS_5 x S^5 string in the AdS/CFT correspondence. For this we extend the
previous construction in the su(1|2) subsector due to Janik to the full algebra
by specifying the action of the coproduct and the antipode on the remaining
generators. The nontriviality of the coproduct is determined by length-changing
effects and results in an unusual central braiding. As an application we
explicitly determine the antiparticle representation by means of the
established antipode.Comment: 12 pages, no figures, minor changes, typos corrected, comments and
references added, v3: three references adde
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