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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Some recurrence formulas for spherical polynomials on tube domains
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by Gen Kai Zhang PDF
Trans. Amer. Math. Soc. 347 (1995), 1725-1734 Request permission

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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • 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