513 research outputs found
Spherical and Cherednik-Opdam transforms of Jacobi-type polynomials
No full textThe spherical transform maps the orthogonal basis of symmetric Jacobi-type polynomials to an orthogonal basis of (symmetric) Wilson polynomials. The spherical transform is closely related to the Cherednik-Opdam transform, as it is essentially its symmetric version. The symmetric Jacobi-type polynomials can be composed from the non-symmetric Jacobi-type polynomials. These relations, between the symmetric and non-symmetric theory, give an incentive to consider the Cherednik-Opdam transform of non-symmetric Jacobi-type polynomials. This work gives an overview of the symmetric theory about the spherical transform of Jacobi-type polynomials and lays down the groundwork for the Cherednik-Opdam transform of the non-symmetric Jacobi-type polynomials
Restoration survival. Patient or dentist, who is key?
No full textContains fulltext :
201886.pdf (Publisher’s version ) (Open Access)Radboud University, 12 april 2019Promotor : Huysmans, M.C.D.N.J.M. Co-promotores : Opdam, N.J.M., Braspenning, J.C.C
On the unramified spherical automorphic spectrum
No full textThis thesis contains two results on harmonic analysis of reductive groups. First, let G be connected and defined over a number field F, A be the ring of adèles and K be a maximal compact subgroup of G(A). We studied the decomposition of the space of square-integrable functions on the quotient G(F)\G(A)/K, as a module for a global Hecke algebra. Similar results than the ones obtained here have been established by various authors for many special cases of reductive groups. The main feature of the present approach is the fact that it is uniform. Such approach was greatly inspired by results of G. Heckman and E. Opdam in treating spectral problems for graded affine Hecke algebras. In the proof, we need a result by M. Reeder on the weight spaces of the (anti)spherical discrete series representations of affine Hecke algebras, as well as we are faced with the problem of computing certain rational constants factors involved in the global spectral measure in terms of local Plancherel measures which are known only in the affine Hecke algebra context. As for the second result, we show that a Coxeter complex and a Euclidean building can be endowed with piecewise linear Morse functions that allows one to write down explicit contractions of the underlying cell complexes. Such approach via PL Morse theory to study buildings was heavily inspired by ideas from G. Savin and M. Bestvina in the specific case of the building of SL(n). We conjecture that these contractions have nice bounds on their coefficients and thus can be used to compute Ext groups between tempered representations in an analogous way as was done by M. Solleveld and E. Opdam
Discrete series characters for affine Hecke algebras and their formal degrees
No full textWe introduce the generic central character of an irreducible discrete series representation of an affine Hecke algebra. Using this invariant we give a new classification of the irreducible discrete series characters for all abstract affine Hecke algebras (except for the types , n=6, 7, 8) with arbitrary positive parameters and we prove an explicit product formula for their formal degrees (in all cases)
From representations of the rational Cherednik algebra to parabolic Hilbert schemes via the Dunkl-Opdam subalgebra
No full textIn this note we explicitly construct an action of the rational Cherednik
algebra corresponding to the permutation
representation of on the -equivariant homology of
parabolic Hilbert schemes of points on the plane curve singularity for coprime and . We use this to construct actions of quantized
Gieseker algebras on parabolic Hilbert schemes on the same plane curve
singularity, and actions of the Cherednik algebra at on the equivariant
homology of parabolic Hilbert schemes on the non-reduced curve
Our main tool is the study of the combinatorial representation theory of the
rational Cherednik algebra via the subalgebra generated by Dunkl-Opdam
elements.Comment: 63 pages; This version fixes a couple of mistakes in Propositions
7.19 and 8.9 from the published version, concerning the use of dual lattices.
The article title in v3 has also change
Opzet bij ziekte en het voorkomen van arbeidsongeschiktheid: een onrechtvaardig verschil
No full textDe zieke werknemer heeft geen recht op loondoorbetaling indien hij zijn ziekte door opzet heeft veroorzaakt. De WIA verplicht de verzekerde om het ontstaan van arbeidsongeschiktheid te voorkomen, voor zover dit redelijkerwijs van hem verwacht mag worden. Het BW en de WIA kennen derhalve een verschillend criterium om eigen schuld van de betrokkene aan het ontstaan van arbeidsongeschiktheid toe te rekenen. In deze bijdrage wordt dit verschil besproken en wordt bezien of er voor dit verschil een rechtvaardiging bestaat
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