10,634 research outputs found
The Topology of Foliations Formed by the Generic K-Orbits of a Subclass of the Indecomposable MD5-Groups
The present paper is a continuation of [13], [14] of the authors.
Specifically, the paper considers the MD5-foliations associated to connected
and simply connected MD5-groups such that their Lie algebras have 4-dimensional
commutative derived ideal. In the paper, we give the topological classification
of all considered MD5-foliations. A description of these foliations by certain
fibrations or suitable actions of and the Connes' C*-algebras
of the foliations which come from fibrations are also given in the paper.Comment: 20 pages, no figur
Asymptotic Lattices, Good Labellings, and the Rotation Number for Quantum Integrable Systems
This article introduces the notion of good labellings for asymptotic lattices
in order to study joint spectra of quantum integrable systems from the point of
view of inverse spectral theory. As an application, we consider a new spectral
quantity for a quantum integrable system, the quantum rotation number. In the
case of two degrees of freedom, we obtain a constructive algorithm for the
detection of appropriate labellings for joint eigenvalues, which we use to
prove that, in the semiclassical limit, the quantum rotation number can be
calculated on a joint spectrum in a robust way, and converges to the well-known
classical rotation number. The general results are applied to the semitoric
case where formulas become particularly natural
Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials
The concept of cyclic tridiagonal pairs is introduced, and explicit examples
are given. For a fairly general class of cyclic tridiagonal pairs with
cyclicity N, we associate a pair of `divided polynomials'. The properties of
this pair generalize the ones of tridiagonal pairs of Racah type. The algebra
generated by the pair of divided polynomials is identified as a higher-order
generalization of the Onsager algebra. It can be viewed as a subalgebra of the
q-Onsager algebra for a proper specialization at q the primitive 2Nth root of
unity. Orthogonal polynomials beyond the Leonard duality are revisited in light
of this framework. In particular, certain second-order Dunkl shift operators
provide a realization of the divided polynomials at N=2 or q=i.Comment: 32 pages; v2: Appendices improved and extended, e.g. a proof of
irreducibility is added; v3: version for Linear Algebra and its Applications,
one assumption added in Appendix about eq. (A.2
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