381 research outputs found
Intertwining operator for Calogero-Moser-Sutherland system
We consider generalised Calogero-Moser-Sutherland quantum Hamiltonian
associated with a configuration of vectors on the plane which is a union
of and root systems. The Hamiltonian depends on one parameter.
We find an intertwining operator between and the Calogero-Moser-Sutherland
Hamiltonian for the root system . This gives a quantum integral for of
order 6 in an explicit form thus establishing integrability of .Comment: 24 page
On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups
In this paper, we consider the relation between two nonabelian Fourier
transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig
parameters for unipotent elliptic representations of a split p-adic group and
the second is defined in terms of the pseudocoefficients of these
representations and Lusztig's nonabelian Fourier transform for characters of
finite groups of Lie type. We exemplify this relation in the case of the p-adic
group of type G_2.Comment: 17 pages; v2: several minor corrections, references added; v3:
corrections in the table with unipotent discrete series of G
Extensions of tempered representations
Let be irreducible tempered representations of an affine Hecke
algebra H with positive parameters. We compute the higher extension groups
explicitly in terms of the representations of analytic
R-groups corresponding to and . The result has immediate
applications to the computation of the Euler-Poincar\'e pairing ,
the alternating sum of the dimensions of the Ext-groups. The resulting formula
for is equal to Arthur's formula for the elliptic pairing of
tempered characters in the setting of reductive p-adic groups. Our proof
applies equally well to affine Hecke algebras and to reductive groups over
non-archimedean local fields of arbitrary characteristic. This sheds new light
on the formula of Arthur and gives a new proof of Kazhdan's orthogonality
conjecture for the Euler-Poincar\'e pairing of admissible characters.Comment: This paper grew out of "A formula of Arthur and affine Hecke
algebras" (arXiv:1011.0679). In the second version some minor points were
improve
Jack polynomials with prescribed symmetry and hole propagator of spin Calogero-Sutherland model
We study the hole propagator of the Calogero-Sutherland model with SU(2)
internal symmetry. We obtain the exact expression for arbitrary non-negative
integer coupling parameter and prove the conjecture proposed by one of
the authors. Our method is based on the theory of the Jack polynomials with a
prescribed symmetry.Comment: 12 pages, REVTEX, 1 eps figur
On frequencies of small oscillations of some dynamical systems associated with root systems
In the paper by F. Calogero and author [Commun. Math. Phys. 59 (1978)
109-116] the formula for frequencies of small oscillations of the Sutherland
system ( case) was found. In present note the generalization of this
formula for the case of arbitrary root system is given.Comment: arxiv version is already officia
Common Algebraic Structure for the Calogero-Sutherland Models
We investigate common algebraic structure for the rational and trigonometric
Calogero-Sutherland models by using the exchange-operator formalism. We show
that the set of the Jack polynomials whose arguments are Dunkl-type operators
provides an orthogonal basis for the rational case.Comment: 7 pages, LaTeX, no figures, some text and references added, minor
misprints correcte
New Algebraic Quantum Many-body Problems
We develop a systematic procedure for constructing quantum many-body problems
whose spectrum can be partially or totally computed by purely algebraic means.
The exactly-solvable models include rational and hyperbolic potentials related
to root systems, in some cases with an additional external field. The
quasi-exactly solvable models can be considered as deformations of the previous
ones which share their algebraic character.Comment: LaTeX 2e with amstex package, 36 page
Conventional bitewing radiography
Accurate detection and diagnosis of carious lesions is the prerequisite for application of the most effective caries management approach. However, the accuracy of proximal caries detection using visual-tactile assessment is limited. Additional diagnostic measures should therefore be performed to increase the validity of the diagnosis. Amongst various caries detection aids available, bitewing radiographs remain the gold standard for detection of proximal caries lesions. Here we describe a method for caries diagnosis using standardized bitewing holders. With this method the bitewing holders can be placed more precisely and reproducibly in the oral cavity. This approach increases accuracy of bitewing radiographs, which, due to the reproducible placement of the x-ray film, allows for monitoring of carious lesions long term
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