161 research outputs found
Braiding for the quantum gl_2 at roots of unity
In our preceding papers we started considering the categories of tangles with
flat G-connections in their complements, where G is a simple complex algebraic
group. The braiding (or the commutativity constraint) in such categories
satisfies the holonomy Yang-Baxter equation and it is this property which is
essential for our construction of invariants of tangles with flat G-connections
in their complements. In this paper, to any pair of irreducible modules over
the quantized universal enveloping algebra of gl_2 at a root of unity, we
associate a solution of the holonomy Yang-Baxter equation.Comment: 18 pages, 1 figur
Affine Toda field theory as a 3-dimensional integrable system
The affine Toda field theory is studied as a 2+1-dimensional system. The
third dimension appears as the discrete space dimension, corresponding to the
simple roots in the affine root system, enumerated according to the
cyclic order on the affine Dynkin diagram. We show that there exists a
natural discretization of the affine Toda theory, where the equations of motion
are invariant with respect to permutations of all discrete coordinates. The
discrete evolution operator is constructed explicitly. The thermodynamic Bethe
ansatz of the affine Toda system is studied in the limit . Some
conjectures about the structure of the spectrum of the corresponding discrete
models are stated.Comment: 17 pages, LaTe
Torus Knot and Minimal Model
We reveal an intimate connection between the quantum knot invariant for torus
knot T(s,t) and the character of the minimal model M(s,t), where s and t are
relatively prime integers. We show that Kashaev's invariant, i.e., the
N-colored Jones polynomial at the N-th root of unity, coincides with the
Eichler integral of the character.Comment: 10 page
Tetrahedral forms in monoidal categories and 3-manifold invariants
We introduce systems of objects and operators in linear monoidal categories called -systems. A -system satisfying several additional assumptions gives rise to a topological invariant of triples (a closed oriented 3-manifold , a principal bundle over , a link in ). This construction generalizes the quantum dilogarithmic invariant of links appearing in the original formulation of the volume conjecture. We conjecture that all quantum groups at odd roots of unity give rise to -systems and we verify this conjecture in the case of the Borel subalgebra of quantum sl
Laser beam welding of a CoCrFeNiMn-type high entropy alloy produced by self-propagating high-temperature synthesis
Fiber laser beam welding of a CoCrFeNiMn-type high entropy alloy (HEA) produced by self-propagating hightemperature synthesis (SHS) was reported in this work. The SHS-fabricated alloy was characterized by both ∼2 times reduced Mn content in comparison with that of the other principal components and the presence of impurities including Al, C, S, and S
Three-Dimensional Integrable Models and Associated Tangle Invariants
In this paper we show that the Boltzmann weights of the three-dimensional
Baxter-Bazhanov model give representations of the braid group, if some suitable
spectral limits are taken. In the trigonometric case we classify all possible
spectral limits which produce braid group representations. Furthermore we prove
that for some of them we get cyclotomic invariants of links and for others we
obtain tangle invariants generalizing the cyclotomic ones.Comment: Number of pages: 21, Latex fil
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