32,866 research outputs found
Set-theoretical solutions to the Yang-Baxter Relation from factorization of matrix polynomials and -functions
New set-theoretical solutions to the Yang-Baxter Relation are constructed.
These solutions arise from the decompositions "in different order" of matrix
polynomials and -functions. We also construct a "local action of the
symmetric group" in these cases, generalizations of the action of the symmetric
group given by the set-theoretical solution.Comment: 9 pages, to appear in Moscow Math Journa
Factoring in the hyperelliptic Torelli group
The hyperelliptic Torelli group is the subgroup of the mapping class group
consisting of elements that act trivially on the homology of the surface and
that also commute with some fixed hyperelliptic involution. The authors and
Putman proved that this group is generated by Dehn twists about separating
curves fixed by the hyperelliptic involution. In this paper, we introduce an
algorithmic approach to factoring a wide class of elements of the hyperelliptic
Torelli group into such Dehn twists, and apply our methods to several basic
elements.Comment: 9 pages, 7 figure
Representations of the Weyl group and Wigner functions for SU(3)
Bases for SU(3) irreps are constructed on a space of three-particle tensor
products of two-dimensional harmonic oscillator wave functions. The Weyl group
is represented as the symmetric group of permutations of the particle
coordinates of these space. Wigner functions for SU(3) are expressed as
products of SU(2) Wigner functions and matrix elements of Weyl transformations.
The constructions make explicit use of dual reductive pairs which are shown to
be particularly relevant to problems in optics and quantum interferometry.Comment: : RevTex file, 11 pages with 2 figure
Polynomial solutions to Hâ problems
The paper presents a polynomial solution to the standard Hâ-optimal control problem. Based on two polynomial J-spectral factorization problems, a parameterization of all suboptimal compensators is obtained. A bound on the McMillan degree of suboptimal compensators is derived and an algorithm is formulated that may be used to solve polynomial J-spectral factorization problems
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