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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Some recurrence formulas for spherical polynomials on tube domains


Author: Gen Kai Zhang
Journal: Trans. Amer. Math. Soc. 347 (1995), 1725-1734
MSC: Primary 22E46; Secondary 33C55, 65D15
DOI: https://doi.org/10.1090/S0002-9947-1995-1249896-7
MathSciNet review: 1249896
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Abstract: For a tube domain $ G/K$ we study the tensor products of two spherical representations of the maximal compact group $ K$ and the product of the corresponding spherical polynomials. When one of these is a fundamental representation, we prove that the spherical representations appear with multiplicity at most one and we then find all the coefficients in the recurrence formula for the product of the spherical polynomials. This generalizes the previous result of L. Vretare and proves for certain cases a conjecture of R. Stanley on Jack symmetric polynomials.


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DOI: https://doi.org/10.1090/S0002-9947-1995-1249896-7
Keywords: Tube domain, recurrence formula, spherical polynomial
Article copyright: © Copyright 1995 American Mathematical Society