"). 

 4. van Dijk, On a class of generalized Gelfand pairs, Math. Z. 193, 581-593 (1986). 

 5. D. Prasad, Trilinear forms for representations of GL2 and local ? factors, Compositio 
 Mathematica 75, N.1, 1-46 (1990). 
 (N.S.) 24, no. 2, 277?301 (1991). 

 6.  E.G.F. Thomas, The theorem of Bochner-Schwartz-Godement for generalized Gelfand pairs, 
 Functional Analysis: Surveys and results III, Bierstedt, K.D., Fuchsteiner, B. (eds.), Elsevier 
 Science Publishers B.V. (North Holland) 

 7. E. E H. Bosman and G. Van Dijk, A New Class of Gelfand Pairs, Geometriae Dedicata 
 50, 261-282, 261 @ 1994 KluwerAcademic Publishers. Printed in the Netherlands (1994). 

 8. H. Jacquet, S. Rallis, Uniqueness of linear periods., Compositio Mathematica , tome 102, 
 n.o. 1 , p. 65-123 (1996) 

 9. B. Gross, Some applications of Gelfand pairs to number theory, Bull. Amer. Math. Soc. 
 (N.S.) 24, no. 2, 277?301 (1991). 
 1971), pp. 95?118. Halsted, New York (1975).Hi I have severld remarks 

 1. exsampel 3 is a gel. pair only in waider sens then the difinition abuve, bcose SL(n-1,C) is not compact. more exactly it's gel par in the sens that any irdusebale ""admisebale smothe freshe"" represantation of G have not more than 1-dimantional spais of K-invariant functionals. (formaly , to the bast of my knowlig, in this case it's proven only for the case of pre-uinitaru reps. but I'm shoore it's can be done esely using the tecnic developet in the referense below) .\ 

 2. the last asertion abut multiplisity 1 of the restriction is troo only conjecturaly. also thay have nothing to with the fact that the pair (SL(n,C),SL(n-1,C)) is gelfand. this property of mult. 1 usualy cald strong gel. pair, and it's equivalent to the fact that (K x G, \delta K) is gelfand pair (hire \delta H is the diagonal imbading of K in K x G).  

 3. in general , to the best of my knowlig, the sphirical property is a nesesary condition for being gel. howeever it is not sufitiant. also it refer jast to the caise that G is redactive (more exactly: points of alg. redactive grupe over sume local fild) 

 4. her some of refernses on gel. pair (I'm not share that they r apropriat to the artical becose thay r not baisic enaght, also I'm an outor of them so I'm not objectiv)  

 a. arXiv:0709.1273,  (GL(n+1,F),GL(n,F)) is a Gelfand pair for any local field F, Avraham Aizenbud, Dmitry Gourevitch, Eitan Sayag 

 b. arXiv:0711.1471, (O(V+F), O(V)) is a Gelfand pair for any quadratic space V over a local field F, Avraham Aizenbud, Dmitry Gourevitch, Eitan Sayag 

 c. arXiv:0709.4215, Multiplicity one Theorems, Avraham Aizenbud, Dmitry Gourevitch, Steve Rallis, Gérard Schiffmann 

 e. arXiv:0803.3395, Generalized Harish-Chandra descent and applications to Gelfand pairs, Avraham Aizenbud, Dmitry Gourevitch  

 f. arXiv:0803.3397, An archimedean analog of Jacquet - Rallis theorem, Avraham Aizenbud, Dmitry Gourevitch 

 g. arXiv:0805.2504, Some regular symmetric pairs,Avraham Aizenbud, Dmitry Gourevitch 

 5. unfortionatly I can't edit the artical becose of my teribale spaling and very wike english 

 ==other refs== 

 hier r same other referenses [1] below may serv as a good exposition for the cais K is compact lie group , [a] abave contains a good exposition for non  compact K mainly for the lie gruop caise but also for the p-adic analog. so I think both of them shold b inkloded in the artical. However non of them is the ""canonical referens for gelfand pairs"" so one should stil find some beter refernse. 

 all ather referenses (above and below) are mostly contain prove of gel. property for some pairs. may b some of them may be aded to the artical but only as a ""aditonal riding"". may be after some one will rote a list of knoen gelfand pairs, those refernses can be aded to this list  

 1. OKSANA YAKIMOVA, PRINCIPAL GELFAND PAIRS,  Transformation Groups, Vol. 11, No. 2, 2006, (http://www.springerlink.com/content/p6441x3455367h17/) 

 2. I.M. Gelfand, D. Kazhdan, Representations of the group GL(n,K) where K is a local field, 
 Lie groups and their representations (Proc. Summer School, Bolyai Janos Math. Soc., Budapest, 
 1971), pp. 95?118. Halsted, New York (1975). 
 c 
 3. J. Shalika, The multiplicity one theorem for GLn, Annals of Mathematics , 100, N.2, 171- 
 193 (1974). 

 4. van Dijk, On a class of generalized Gelfand pairs, Math. Z. 193, 581-593 (1986). 

 5. D. Prasad, Trilinear forms for representations of GL2 and local ? factors, Compositio 
 Mathematica 75, N.1, 1-46 (1990). 
 (N.S.) 24, no. 2, 277?301 (1991). 

 6.  E.G.F. Thomas, The theorem of Bochner-Schwartz-Godement for generalized Gelfand pairs, 
 Functional Analysis: Surveys and results III,