logo AFST
Harish-Chandra’s c-function; 50 years later
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 2-3, pp. 385-402.

Nous discutons différents aspects de la fonction c de Harish-Chandra, en soulignant ses interactions avec la transformée horosphérique.

We discuss different aspects of the c-function of Harish-Chandra with focus on its connection with the horospherical transform.

@article{AFST_2016_6_25_2-3_385_0,
     author = {Simon Gindikin},
     title = {Harish-Chandra{\textquoteright}s $c$-function; 50 years later},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {385--402},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 25},
     number = {2-3},
     year = {2016},
     doi = {10.5802/afst.1498},
     mrnumber = {3530162},
     zbl = {1353.22005},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1498/}
}
TY  - JOUR
AU  - Simon Gindikin
TI  - Harish-Chandra’s $c$-function; 50 years later
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2016
DA  - 2016///
SP  - 385
EP  - 402
VL  - Ser. 6, 25
IS  - 2-3
PB  - Université Paul Sabatier, Toulouse
UR  - https://afst.centre-mersenne.org/articles/10.5802/afst.1498/
UR  - https://www.ams.org/mathscinet-getitem?mr=3530162
UR  - https://zbmath.org/?q=an%3A1353.22005
UR  - https://doi.org/10.5802/afst.1498
DO  - 10.5802/afst.1498
LA  - en
ID  - AFST_2016_6_25_2-3_385_0
ER  - 
%0 Journal Article
%A Simon Gindikin
%T Harish-Chandra’s $c$-function; 50 years later
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2016
%P 385-402
%V Ser. 6, 25
%N 2-3
%I Université Paul Sabatier, Toulouse
%U https://doi.org/10.5802/afst.1498
%R 10.5802/afst.1498
%G en
%F AFST_2016_6_25_2-3_385_0
Simon Gindikin. Harish-Chandra’s $c$-function; 50 years later. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 2-3, pp. 385-402. doi : 10.5802/afst.1498. https://afst.centre-mersenne.org/articles/10.5802/afst.1498/

[1] Akhiezer (D.N.), Gindikin (S.G.).— On Stein extensions of real symmetric spaces, Math. Ann., 286 p. 1-12 (1990). | Article | MR 1032920 | Zbl 0681.32022

[2] Beerends (R.J.).— The Fourier transform of Harish-Chandra’s c-function and inversion of Abel transform, Math. Ann., 277 1 p. 1-23 (1987). | Article | Zbl 0597.43006

[3] Braverman (A.), Finkelberg (M.), Kazhdan (D.).— Affine Gindikin-Karpelevich formula via Uhlenbeck spaces, arXiv:0912.5132 [math.RT] (2009). | Article

[4] Braverman (A.), Garland (H.), Kazhdan (D.), Patnaik (M.).— An affine Gindikin-Karpelevich formula, arXiv:1212.6473 [math.RT] (2012). | Article

[5] DeConcini (C.),Procesi (C.).— Complete symmetric varieties, Lecture Notes in Math., 996 p. 1-44 (1983).

[6] Gelfand (I.M.), Graev (M.I.).— Geometry of homogeneous spaces, representations of groups in homogeneous spaces and related questions of integral geometry, Amer. Math. Transl. (2), 37 p. 351-429 (1964).

[7] Gindikin (S.).— Integral geometry on symmetric manifolds, Amer. Math. Transl. (2), 148 p. 29-37 (1991). | Article

[8] Gindikin (S.).— Holomorphic language for ¯-cohomology and representations of real semisimple Lie groups, The Penrose Transform and Analytic Cohomology in Representation Theory (M. Eastwood, J. Wolf, R. Zierau, eds), 154, Cont. Math., Amer. Math. Soc., p. 103-115 (1993). | Article | Zbl 0808.55006

[9] Gindikin (S.).— Integral geometry on SL(2,), Math. Research Letters, 7 p. 1-15 (2000). | Article | MR 1783620 | Zbl 0968.22014

[10] Gindikin (S.).— Product-formula for c-function and inverse horospherical transform, Amer. Math. Soc. Transl. (2), 210 p. 125-134 (2003). | Article | Zbl 1044.01012

[11] Gindikin (S.).— Harmonic analysis on symmetric manifolds from the point of view of complex analysis, Japanese J. Math., 1, 1 p. 87-105 (2006). | Article | MR 2261062 | Zbl 1159.22004

[12] Gindikin (S.).— The integral Cauchy formula on symmetric Stein manifolds, Colloquium de Giorgi, p. 19-28, Edizione della Normale (2006). | Zbl 1129.32006

[13] Gindikin (S.).— Horospherical transform on Riemannian symmetric manifolds of noncompact type, Funct. Anal. Appl., 42, 4 p. 1-11 (2008). | Article | Zbl 1159.22008

[14] Gindikin (S.).— Helgason’s conjecture in complex analytical interior, Representation Theory, Complex Analysis and Integral Geometry (B. Krotz, O. Offen, E. Sayag, eds), Birkhauser p. 87-96 (2010). | Article

[15] Gindikin (S.).— Harmonic analysis on symmetric spaces as complex analysis, Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro (Cogdell, Shahidi, and Soudry, eds), AMS, Contemporary Math., 614 p. 69-80 (2014). | Article | Zbl 1306.22003

[16] Gindikin (S.).— Local inversion formulas for horospherical transforms, Moscow Math. J., 13, 2 p. 267-280 (2013). | Article | MR 3134907 | Zbl 1298.22013

[17] Gindikin (S.).— Intermediate horospherical transforms, wonderful compactification and c-functions, to appear. | Article | MR 3134907

[18] Gindikin (S.), Goodman (R.).— Restricted roots and restricted form of the Weyl dimension formula for spherical varieties, J. Lie Theory, 13, 1 p. 257-311 (2013).

[19] Gindikin (S.G.), Karpelevich (F.I.).— Plancherel measure for symmetric spaces of non-positive curvature, Sovjet Math. Dokl., 3 p. 962-965 (1962). | Zbl 0156.03201

[20] Gindikin (S.G.), Karpelevich (F.I.).— A problem of integral geometry, In memoriam: N. G. Chebotarev, Izdat. Kazan. Univ. p. 30-43 (1964), English transl. in, Selecta Math. Sov., 1p. 169-184 (1981).

[21] Gindikin (S.G.), Karpelevich (F.I.).— On a integral connected with symmetric Riemann spaces of of nonpositive curvature, Izv. Akad Nauk SSSR Ser. Mat., 30 p. 1147-1156 (1966), English transl. in, Amer. Math. Soc. Transl. (2), 85 p. 249-258 (1969). | Article

[22] Harish-Chandra.— Spherical functions on a semisimple Lie group. I,II, Americamn J. Math., 80 p. 241-310, 553-613 (1958). | Article | MR 101279

[23] Helgason (S.).— Groups and Geometric Analysis, Academic Press (1984). | Article

[24] Hilgert (J.), Pasquale (A.), Vinberg (E.).— The dual horospherical Radon transform for polynomials, Moscow Math. J., 2 p. 113-126 (2002). | Article | MR 1900587 | Zbl 1003.43008

[25] Knapp (A.W.), Stein (E.M.).— Intertwining operators for semisimple groups, Annals Math., 93 p. 489-578 (1971). | Article | Zbl 0257.22015

[26] Macdonald (I.G.).— Spherical functions on a group of p-adic type, Ramanujan Institute lecture notes 2. Madras (1971). | Zbl 0302.43018

[27] Olafsson (G.), Pasquale (A.).— Ramanujan’s Master Theorem for the hypergeometric Fourier transform on root systems, J. Fourier Anal. Appl., 19 6 p. 1150-1183 (2013). | Article | MR 3132909 | Zbl 1314.43002

[28] Oshima (T.).— A realization of of Riemannian symmetric spaces, J. Math Soc. Japan, 30 (1978) p. 117-132. | Article | MR 477175 | Zbl 0364.43010

[29] Vinberg (E.).— On reductive algebraic semigroups, Amer.Math.Soc. Transl., 169 p. 145-182 (1995). | Article | Zbl 0840.20041

Cité par Sources :