Recent Research Publications

  1. View/Download Postscript format file View/Download PDF format file Combinatorics and spherical functions on the Heisenberg group, (with G. Ratcliff), Representation Theory, vol 2, 79-105, 1998.
  2. View/Download Postscript format file View/Download PDF format file The spherical transform of a Schwartz function on the Heisenberg group, (with J. Jenkins and G. Ratcliff), Journal of Functional Analysis, vol 154, 379-423, 1998.
  3. View/Download Postscript format file View/Download PDF format file The orbit method and Gelfand pairs associated with nilpotent Lie groups, (with J. Jenkins and G. Ratcliff), Journal of Geometric Analysis, vol 9, 569-582, 1999.
  4. View/Download Postscript format file View/Download PDF format file Rationality of the generalized binomial coefficients for a multiplicity free action, (with G. Ratcliff), Journal of the Australian Math. Soc. (Series A), vol 68, 387-410, 2000.
  5. View/Download Postscript format file View/Download PDF format file Moment sets and the unitary dual of a nilpotent Lie group, (with A. Baklouti and G. Ratcliff), Journal of Lie Theory, vol 11, 135-154, 2001.
  6. View/Download Postscript format file View/Download PDF format file Invariant theory for the orthogonal group via star products (with D. Arnal, O. Boukary Baoua and G. Ratcliff), Journal of Lie Theory, vol 11, 441-458, 2001.
  7. View/Download Postscript format file View/Download PDF format file Three-step harmonic solvmanifolds (with T. Payne and G. Ratcliff), Geometriae Dedicata, vol 101, 103-127, 2003.
  8. View/Download Postscript format file View/Download PDF format file On multiplicity free actions (with G. Ratcliff), in Representations of Real and p-adic Groups, ed. E-C. Tan and C. Zhu, World Scientific Press, 2004. (Based on lectures delivered at the Institute for Mathematical Sciences, National University of Singapore, January 2003.)
  9. View/Download Postscript format file View/Download PDF format file Differential systems of type (1,1) on Hermitian symmetric spaces and their solutions (with D. Buraczewski, E. Damek and G. Ratcliff), Journal of Functional Analysis, vol 215, 427-475, 2004.
  10. View/Download Postscript format file View/Download PDF format file The space of bounded spherical functions on the free two step nilpotent Lie group (with G. Ratcliff), Transformation Groups, vol 13, 243-281, 2008.
  11. View/Download Postscript format file View/Download PDF format file Gelfand pairs associated with finite Heisenberg groups (with G. Ratcliff), in Representations, Wavelets and Frames: A Celebration of the Mathematical Work of Lawrence Baggett(Applied and Numerical Harmonic Analysis), ed. P Jorgensen, K. Merril, J. Packer, Birkhauser, 2008.
  12. View/Download Postscript format file View/Download PDF format file Spherical Functions for the action of a finite unitary group on a finite Heisenberg Group (with G. Ratcliff), Contemporary Mathematics, vol 491, 151-166, 2009.
  13. View/Download Postscript format file View/Download PDF format file Combinatorial properties of generalized binomial coefficients (with G. Ratcliff), Contemporary Mathematics, vol 491, 141-150, 2009.
  14. View/Download Postscript format file View/Download PDF format file Invariant polynomials for multiplicity free actions (with R. Michael Howe and G. Ratcliff), Journal of Lie Theory, vol 19, 771-795, 2009.
  15. View/Download Postscript format file View/Download PDF format file Geometric models for the spectra of certain Gelfand pairs associated with Heisenberg groups (with G. Ratcliff), Annali di Matematica Pura ed Applicata, vol 192, 719-740, 2013 (with Erratum on pages 741-743 of the same journal issue).
  16. View/Download Postscript format file View/Download PDF format file Spaces of bounded spherical functions on Heisenberg groups: Part I (with G. Ratcliff), Annali di Matematica Pura ed Applicata, vol 194, 321-342, 2015. Two Maple worksheets provide details concerning examples treated in section 4.6 of this paper:
    Maple 15 worksheet for the action Sp(6)xU(3):M6,3(C) PDF version of the worksheet
    Maple 15 worksheet for the action Sp(4)xU(4):M4,4(C) PDF version of the worksheet
  17. View/Download Postscript format file View/Download PDF format file Spaces of bounded spherical functions on Heisenberg groups: Part II (with G. Ratcliff), Annali di Matematica Pura ed Applicata, vol 194, 533-561, 2015. The following Maple worksheet gives full details concerning an example treated in section 5.6 of this paper:
    Maple 15 worksheet for the action Sp(4)xSp(4)xU(2)xT:M8,2(C) PDF version of the worksheet
  18. View/Download Postscript format file View/Download PDF format file A family of finite Gelfand pairs associated with wreath products (with G. Ratcliff), to appear in Colloquium Mathematicum.


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