Harish-Chandra's c-function

In mathematics, Harish-Chandra's c-function is a function describing the asymptotic behavior of a spherical function of a Lie group. The Gindikin–Karpelevich formula is a product formula for Harish-Chandra's c-function of a Lie group. It was introduced by Gindikin and Karpelevich (1962, 1969). Macdonald (1968, 1971) and Langlands (1971) found an analogous formula for the c-function of a p-adic Lie group.

References

- Doran, Robert S.; Varadarajan, V. S., eds. (2000), "The mathematical legacy of Harish-Chandra", Proceedings of the AMS Special Session on Representation Theory and Noncommutative Harmonic Analysis, held in memory of Harish-Chandra on the occasion of the 75th anniversary of his birth, in Baltimore, MD, January 9–10, 1998, Proceedings of Symposia in Pure Mathematics, vol. 68, Providence, R.I.: American Mathematical Society, pp. xii+551, ISBN 978-0-8218-1197-9, MR 1767886
Gindikin, S. G.; Karpelevich, F. I. (1962), "Plancherel measure for symmetric Riemannian spaces of non-positive curvature", Soviet Math. Dokl., 3: 962–965, ISSN 0002-3264, MR 0150239
Gindikin, S. G.; Karpelevich, F. I. (1969) [1966], "On an integral associated with Riemannian symmetric spaces of non-positive curvature", Twelve Papers on Functional Analysis and Geometry, American Mathematical Society translations, vol. 85, pp. 249–258, ISBN 978-0-8218-1785-8, MR 0222219
Knapp, Anthony W. (2003), "The Gindikin-Karpelevič formula and intertwining operators", in Gindikin, S. G. (ed.), Lie groups and symmetric spaces. In memory of F. I. Karpelevich, Amer. Math. Soc. Transl. Ser. 2, vol. 210, Providence, R.I.: American Mathematical Society, pp. 145–159, ISBN 978-0-8218-3472-5, MR 2018359
Langlands, Robert P. (1971) [1967], Euler products, Yale University Press, ISBN 978-0-300-01395-5, MR 0419366
Macdonald, I. G. (1968), "Spherical functions on a p-adic Chevalley group", Bulletin of the American Mathematical Society, 74 (3): 520–525, doi:10.1090/S0002-9904-1968-11989-5, ISSN 0002-9904, MR 0222089{{citation}}: CS1 maint: MR format (link)
Macdonald, I. G. (1971), Spherical functions on a group of p-adic type, Ramanujan Institute lecture notes, vol. 2, Ramanujan Institute, Centre for Advanced Study in Mathematics,University of Madras, Madras, MR 0435301