Orthogonal functions generalizing Jack polynomials
| dc.creator | Griffeth, Stephen | |
| dc.date | 2007-07-02 | |
| dc.date | 2008-11-09 | |
| dc.date.accessioned | 2026-07-07T10:16:39Z | |
| dc.date.available | 2026-07-07T10:16:39Z | |
| dc.description | The rational Cherednik algebra $\HH$ is a certain algebra of differential-reflection operators attached to a complex reflection group $W$. Each irreducible representation $S^λ$ of $W$ corresponds to a standard module $M(λ)$ for $\HH$. This paper deals with the infinite family $G(r,1,n)$ of complex reflection groups; our goal is to study the standard modules using a commutative subalgebra $\ttt$ of $\HH$ discovered by Dunkl and Opdam. In this case, the irreducible $W$-modules are indexed by certain sequences $λ$ of partitions. We first show that $\ttt$ acts in an upper triangular fashion on each standard module $M(λ)$, with eigenvalues determined by the combinatorics of the set of standard tableaux on $λ$. As a consequence, we construct a basis for $M(λ)$ consisting of orthogonal functions on $\CC^n$ with values in the representation $S^λ$. For $G(1,1,n)$ with $λ=(n)$ these functions are the non-symmetric Jack polynomials. We use intertwining operators to deduce a norm formula for our orthogonal functions and give an explicit combinatorial description of the lattice of submodules of $M(λ)$ in the case in which the orthogonal functions are all well-defined. | |
| dc.description | 21 pages; revised version contains a combinatorial description of the set of submodules of each standard module; 2nd revision uses Clifford theory to relate G(r,p,n) Cherednik algebra to that for G(r,1,n) | |
| dc.identifier | https://arxiv.org/abs/0707.0251 | |
| dc.identifier | http://arxiv.org/abs/0707.0251 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173581 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.title | Orthogonal functions generalizing Jack polynomials | |
| dc.type | text |