Multidimensional Hahn polynomials, intertwining functions on the symmetric group and Clebsch-Gordan coefficients
نویسنده
چکیده
We generalize a construction of Dunkl, obtaining a wide class intertwining functions on the symmetric group and a related family of multidimensional Hahn polynomials. Following a suggestion of Vilenkin and Klymik, we develop a tree-method approach for those intertwining functions. We also give a group theoretic proof of the relation between Hahn polynomials and Clebesh-Gordan coefficients, given analytically by Koornwinder and by Nikiforov, Smorodinskĭi and Suslov. Such relation is also extended to the multidimensional case. 1
منابع مشابه
N ov 2 00 7 Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of
Representations of the quantum superalgebra U q [osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U q [osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and it is observed that they may be ex...
متن کاملMeixner Functions and Polynomials Related to Lie Algebra Representations
The decomposition of the tensor product of a positive and a negative discrete series representation of the Lie algebra su(1, 1) is a direct integral over the principal unitary series representations. In the decomposition discrete terms can occur, and the discrete terms are a finite number of discrete series representations or one complementary series representation. The interpretation of Meixne...
متن کاملFusion and exchange matrices for quantized sl(2) and associated q-special functions
The aim of this paper is to evaluate in terms of q-special functions the objects (intertwining map, fusion matrix, exchange matrix) related to the quantum dynamical Yang-Baxter equation (QDYBE) for infinite dimensional representations (Verma modules) of the quantized universal enveloping algebra Uq(g) in the case g = sl(2,C). This study is done in the framework of the exchange construction, ini...
متن کاملDiagonal multi - matrix correlators and BPS operators in N = 4 SYM
We present a complete basis of multi-trace multi-matrix operators that has a diagonal two point function for the free matrix field theory at finite N . This generalises to multiple matrices the single matrix diagonalisation by Schur polynomials. Crucially, it involves intertwining the gauge group U(N) and the global symmetry group U(M) with Clebsch-Gordan coefficients of symmetric groups Sn. Wh...
متن کامل9 J an 2 00 7 Representations of U q [ osp ( 1 / 2 ) ] and Basic Hypergeometric Functions
Representations of the quantum superalgebra U q [osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U q [osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and it is observed that they may be ex...
متن کامل