Intertwining operators and polynomials associated with the symmetric group

DOI10.1007/BF01367762zbMath0912.33007MaRDI QIDQ1273643

Charles F. Dunkl

Publication date: 10 May 1999

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178831

zbMATH Keywords

intertwining operatorsymmetric groupJack polynomialsdifferential-difference operator

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Representations of finite symmetric groups (20C30) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Other hypergeometric functions and integrals in several variables (33C70)

Related Items (20)

Special functions and generating functions associated with reflection groups. ⋮ Exact electron addition spectrum in 1d supersymmetric \(t\)-\(J\) model with \(1/r^{2}\) interaction ⋮ Arc spaces and DAHA representations ⋮ The Dunkl kernel and intertwining operator for dihedral groups ⋮ Computing with differential-difference operators ⋮ Nonsymmetric Jack polynomials and integral kernels ⋮ A new plethystic symmetric function operator and the rational compositional shuffle conjecture at \(t=1/q\) ⋮ Convolution operator and maximal function for the Dunkl transform ⋮ Singular polynomials from orbit spaces ⋮ Volume of the set of unistochastic matrices of order 3 and the mean Jarlskog invariant ⋮ The dunkel intertwining operator on spaces of functions and distributions and integral representation of its dual ⋮ Unnamed Item ⋮ Dunkl intertwining operator for symmetric groups ⋮ Parity-Unimodality and a Cyclic Sieving Phenomenon for Necklaces ⋮ Cyclic sieving, necklaces, and bracelets ⋮ Markov processes related with Dunkl operators ⋮ Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras ⋮ Symmetric Jack polynomials from non-symmetric theory ⋮ Symmetric and nonsymmetric Macdonald polynomials ⋮ Representations of rational Cherednik algebras with minimal support and torus knots.

Cites Work

• Integrals of polynomials associated with tableaux and the Garsia-Haiman conjecture
• The Calogero-Sutherland model and generalized classical polynomials
• Some combinatorial properties of Jack symmetric functions
• Harmonic analysis for certain representations of graded Hecke algebras
• Exact operator solution of the Calogero-Sutherland model
• Certain Hypergeometric Series Related to the Root System BC
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• A Class of Generalized Hypergeometric Functions in Several Variables
• Singular Polynomials for Finite Reflection Groups
• Intertwining Operators Associated to the Group S 3
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• Unnamed Item
• Unnamed Item

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