Reflection groups in analysis and applications

DOI10.1007/s11537-008-0819-3zbMath1191.33006OpenAlexW2026203823WikidataQ57444233 ScholiaQ57444233MaRDI QIDQ1043880

Charles F. Dunkl

Publication date: 9 December 2009

Published in: Japanese Journal of Mathematics. 3rd Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11537-008-0819-3

zbMATH Keywords

Dunkl operatorDunkl transformCalogero-Sutherland modelsCoxeter reflection groupsnon-symmetric Jack polynomials

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Groups and algebras in quantum theory and relations with integrable systems (81R12) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80) Orthogonal polynomials and functions associated with root systems (33C52)

Related Items

Free boson realization of the Dunkl intertwining operator in one dimension ⋮ Rationally-extended Dunkl oscillator on the line ⋮ The Dunkl kernel and intertwining operator for dihedral groups ⋮ On Schrödinger oscillatory integrals associated with the Dunkl transform ⋮ Mathematical analysis as required by a tachyonic observer ⋮ Orthogonal polynomials of compact simple Lie groups ⋮ Generalized Fourier transforms \(\mathcal F_{k,a}\) ⋮ Laguerre semigroup and Dunkl operators

Cites Work

• On elliptic Dunkl operators
• A chaotic representation property of the multidimensional Dunkl processes
• Sutherland models for complex reflection groups
• A new construction of Young's seminormal representation of the symmetric groups
• Yet another proof of the addition formula for Jacobi polynomials
• Poisson and Cauchy kernels for orthogonal polynomials with dihedral symmetry
• Markov processes related with Dunkl operators
• Orthogonal polynomials of types \(A\) and \(B\) and related Calogero models
• The Dunkl transform
• A recursion and a combinatorial formula for Jack polynomials
• The Calogero-Sutherland model and generalized classical polynomials
• On the category \(\mathcal O\) for rational Cherednik algebras.
• Reflection groups and orthogonal polynomials on the sphere
• Asymptotic analysis for the Dunkl kernel
• Harmonic analysis for certain representations of graded Hecke algebras
• Positivity of Dunkl's intertwining operator
• Harmonic functions associated to Dunkl operators
• Convolution operator and maximal function for the Dunkl transform
• Generalized ellipsoidal and sphero-conal harmonics
• Towards a characterization of Markov processes enjoying the time-inversion property
• Orthogonal functions generalizing Jack polynomials
• Orthogonal Polynomials on the Sphere with Octahedral Symmetry
• Exact Heisenberg operator solutions for multiparticle quantum mechanics
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• An Addition Theorem for Hahn Polynomials: The Spherical Functions
• Singular Polynomials for Finite Reflection Groups
• Transmutation operators associated with a dunkl type differential-difference operator on the real line and certain of their applications
• The dunkel intertwining operator on spaces of functions and distributions and integral representation of its dual
• DUNKL OPERATORS FOR COMPLEX REFLECTION GROUPS
• Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model
• Dunkl Operator Formalism for Quantum Many-Body Problems Associated with Classical Root Systems
• On the evaluation formula for Jack polynomials with prescribed symmetry
• Topics in quantum integrable systems
• Intertwining Operators Associated to the Group S 3
• AN INTERTWINING OPERATOR FOR THE GROUP B₂
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item