Vector-Valued Polynomials and a Matrix Weight Function with B2-Action
نویسندگان
چکیده
منابع مشابه
Vector-Valued Polynomials and a Matrix Weight Function with B2-Action. II
This is a sequel to [SIGMA 9 (2013), 007, 23 pages], in which there is a construction of a 2 × 2 positive-definite matrix function K(x) on R. The entries of K(x) are expressed in terms of hypergeometric functions. This matrix is used in the formula for a Gaussian inner product related to the standard module of the rational Cherednik algebra for the group W (B2) (symmetry group of the square) as...
متن کاملVector-Valued Polynomials and a Matrix Weight Function with B2-Action
The structure of orthogonal polynomials on R with the weight function |x1 − x2| |x1x2|1e 2 1+x 2 2)/2 is based on the Dunkl operators of type B2. This refers to the full symmetry group of the square, generated by reflections in the lines x1 = 0 and x1− x2 = 0. The weight function is integrable if k0, k1, k0 +k1 > − 1 2 . Dunkl operators can be defined for polynomials taking values in a module o...
متن کاملA Hypergeometric Function Transform and Matrix-valued Orthogonal Polynomials
The spectral decomposition for an explicit second-order differential operator T is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with multiplicity one. The spectral analysis gives rise to a generalized Fourier transform with an explicit hypergeometric function as a kernel. Using Jacobi polynomial...
متن کاملVector Polynomials and a Matrix Weight Associated to Dihedral Groups
The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case for even dihedral groups). The matrix weight function for the Gaussian form is found explicitly by solving a boundary value problem, and then computing the n...
متن کاملVector Valued Macdonald Polynomials
This paper defines and investigates nonsymmetric Macdonald polynomials with values in an irreducible module of the Hecke algebra of type AN−1. These polynomials appear as simultaneous eigenfunctions of Cherednik operators. Several objects and properties are analyzed, such as the canonical bilinear form which pairs polynomials with those arising from reciprocals of the original parameters, and t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2013
ISSN: 1815-0659
DOI: 10.3842/sigma.2013.007