Factorized $$A_2$$-Leonard pair
Copyright policy )Factorized $$A_2$$-Leonard pair
The notion of factorized $A_2$-Leonard pair is introduced. It is defined as a rank 2 Leonard pair, with actions in certain bases corresponding to the root system of the Weyl group $A_2$, and with some additional properties. The functions arising as entries of transition matrices are bivariate orthogonal polynomials (of Tratnik type) with bispectral properties. Examples of factorized $A_2$-Leonard pairs are constructed using classical Leonard pairs associated to families of orthogonal polynomials of the ($q$-)Askey scheme. The most general examples are associated to an intricate product of univariate ($q$-)Hahn and dual ($q$-)Hahn polynomials.
33 pages
bispectrality, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Leonard pairs, Bispectrality, FOS: Physical sciences, Connections of hypergeometric functions with groups and algebras, and related topics, bivariate orthogonal polynomials, Mathematics - Rings and Algebras, Mathematical Physics (math-ph), (\(q\))-Askey scheme, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], Representation type (finite, tame, wild, etc.) of associative algebras, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Bivariate orthogonal polynomials, Mathematics - Classical Analysis and ODEs, Rings and Algebras (math.RA), (q-)Askey scheme, [MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA], Classical Analysis and ODEs (math.CA), FOS: Mathematics, [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], Representation Theory (math.RT), Mathematical Physics, Mathematics - Representation Theory
bispectrality, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Leonard pairs, Bispectrality, FOS: Physical sciences, Connections of hypergeometric functions with groups and algebras, and related topics, bivariate orthogonal polynomials, Mathematics - Rings and Algebras, Mathematical Physics (math-ph), (\(q\))-Askey scheme, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], Representation type (finite, tame, wild, etc.) of associative algebras, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Bivariate orthogonal polynomials, Mathematics - Classical Analysis and ODEs, Rings and Algebras (math.RA), (q-)Askey scheme, [MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA], Classical Analysis and ODEs (math.CA), FOS: Mathematics, [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], Representation Theory (math.RT), Mathematical Physics, Mathematics - Representation Theory
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