An integral for the product of two Selberg-Jack symmetric polynomials

Kevin W. J. Kadell

Compositio Mathematica (1993)

  • Volume: 87, Issue: 1, page 5-43
  • ISSN: 0010-437X

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Kadell, Kevin W. J.. "An integral for the product of two Selberg-Jack symmetric polynomials." Compositio Mathematica 87.1 (1993): 5-43. <http://eudml.org/doc/90228>.

@article{Kadell1993,
author = {Kadell, Kevin W. J.},
journal = {Compositio Mathematica},
keywords = {Selberg's integral; Jack polynomials},
language = {eng},
number = {1},
pages = {5-43},
publisher = {Kluwer Academic Publishers},
title = {An integral for the product of two Selberg-Jack symmetric polynomials},
url = {http://eudml.org/doc/90228},
volume = {87},
year = {1993},
}

TY - JOUR
AU - Kadell, Kevin W. J.
TI - An integral for the product of two Selberg-Jack symmetric polynomials
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 87
IS - 1
SP - 5
EP - 43
LA - eng
KW - Selberg's integral; Jack polynomials
UR - http://eudml.org/doc/90228
ER -

References

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  1. [An2] G.E. Andrews: q-Series: Their Development and Applications in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra, CBMS Regional Conference Series in Mathematics, number 66, American Mathematical Society, Providence, RI, 1986. Zbl0594.33001MR858826
  2. [Ao1] K. Aomoto: Jacobi polynomials associated with Selberg's integral, SIAM J. Math. Analysis18 (1987), 545-549. Zbl0639.33001MR876291
  3. [Hab1] L. Habsieger: Une q-intégrale de Selberg-Askey, SIAM J. Math. Analysis19 (1988), 1475-1489. Zbl0664.33001MR965268
  4. [Han1] P. Hanlon: Jack symmetric functions and some combinatorial properties of Young symmetrizers, J. Combinatorial Theory (A) 47 (1988), 37-80. Zbl0641.20010MR924451
  5. [Hu1] L.K. Hua: Harmonic analysis of functions of several complex variables in the complex domains. Translations of mathematical monographs, Vol. 6, Amer. Math. Soc., Providence, RI, 1963. Zbl0112.07402
  6. [Ja1] H. Jack: A class of symmetric polynomials with a parameter, Proc. Royal Soc. Edinburgh (A)69 (1969-70), 1-17. Zbl0198.04606MR289462
  7. [Ka1] K.W.J. Kadell: A proof of some q-analogues of Selberg's integral for k = 1, SIAM J. Math. Analysis19 (1988), 944-968. Zbl0643.33003MR946654
  8. [Ka2] K.W.J. Kadell: A proof of Askey's conjectured q-analogue of Selberg's integral and a conjecture of Morris, SIAM J. Math. Analysis19 (1988), 969-986. Zbl0643.33004MR946655
  9. [Ka3] K.W.J. Kadell: The q-Selberg polynomials for n = 2, Trans. Amer. Math. Soc.310 (1988), 535-553. Zbl0706.33015MR973170
  10. [Ka4] K.W.J. Kadell: The Selberg-Jack symmetric functions, Advances in Math., to appear. Zbl0885.33009MR1467311
  11. [Ma1] I.G. Macdonald: Symmetric Functions and Hall Polynomials, Oxford University Press, Oxford, 1979. Zbl0487.20007MR553598
  12. [Ma2] I.G. Macdonald: Second edition of [Ma1], to appear. MR1354144
  13. [Ma3] I.G. Macdonald: Orthogonal polynomials associated with root systems, to appear. MR1817334
  14. [Ri1] D. St. P. Richards: Analogs and Extensions of Selberg's integral, Proceedings of the IMA workshop on q-series and partitions, March 1988. Zbl0697.33007
  15. [Se1] A. Selberg: Bemerkninger om et multipelt integral, Norsk. Mat. Tidsskr.26 (1944), 71-78. Zbl0063.06870MR18287
  16. [St1] R.P. Stanley: Some combinatorial properties of Jack symmetric functions, Advances in Math.77 (1989), 76-115. Zbl0743.05072MR1014073
  17. [Sz1] G. Szegö: Orthogonal Polynomials, Colloquium Publications, Vol. 23, American Mathematical Society, Providence, RI, 1975. Zbl0023.21505MR372517
  18. [Ze1] D. Zeilberger: A proof of the G2 case of Macdonald's root system-Dyson conjecture, SIAM J. Math. Analysis18 (1987), 880-883. Zbl0643.05004MR883574

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