Polynomial representation growth and the congruence subgroup problem

Israel Journal of Mathematics

Volumn 144, Issue , 2004, Pages 293-316

  Lubotzky, Alexander ^a   Martin, Benjamin ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 14644390261     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/BF02916715     Document Type: Article

References (25)

1. [BLMM02] H. Bass, A. Lubotzky, A. R. Magid and S. Mozes, Tie proalgebraic completion of rigid groups, Geometriae Dedicata 95 (2002), 19-58.
2. [CR91] C. W. Curtis and I. Reiner, Methods of Representation Theory. Vol. I, Wiley, New York, 1981.
3. [DdSMS99] J. D. Dixon, M. P. F. du Sautoy, A. Mann and D. Segal, Analytic Prop Groups, second edn., Cambridge Studies in Advanced Mathematics, Vol. 61, Cambridge University Press, Cambridge, 1999.
4. [Erd41] P. Erdös, On some asymptotic formulas in the theory of the "factorisation numerorum", Annals of Mathematics 42 (1941), 989-993.
5. [Hum72] J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York, 1972.
6. [JZ03] A. Jaikin-Zapirain, The zeta function of representation of pro-p groups, preprint, 2003.
7. [KL90] P. Kleidman and M. Liebeck, The Subgroup Structure of the Finite Classical Groups, London Mathematical Society Lecture Note Series, Vol. 129, Cambridge University Press, Cambridge, 1990.
8. [Lan93] S. Lang, Algebra, third edn., Addison-Wesley, Reading, MA, 1993.
9. s)-Theorem, in Algebraic Groups and Arithmetic (Mumbai 2001) (S. G.Dani and G. Prasad, eds.), Tata Institute of Fundamental Research Studies in Mathematics, Narosa Publishing House, New Delhi, 2004, pp. 441-468.
10. [LM85] A. Lubotzky and A. R. Magid, Varieties of representations of finitely generated groups, Memoirs of the American Mathematical Society 58 (1985), no. 336, xi+117.
11. [LS94] A. Lubotzky and A. Shalev, On some Λ-analytic pro-p groups, Israel Journal of Mathematics 85 (1994), 307-337.
12. [LS03] A. Lubotzky and D. Segal, Subgroup Growth, Progress in Mathematics, Vol. 212, Birkhäuser Verlag, Basel, 2003.
13. [Lub91] A. Lubotzky, Lattices in rank one Lie groups over local fields, Geometric and Functional Analysis (GAFA) 1 (1991), 406-431.
14. [Lub95] A. Lubotzky, Subgroup growth and congruence subgroups, Inventiones Mathematicae 119 (1995), 267-295.
15. [Mar91] G. A. Margulis, Discrete subgroups of semisimple Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], Vol. 17, Springer-Verlag, Berlin, 1991.
16. [PR93] V. P. Platonov and A. S. Rapinchuk, Abstract properties of S-arithmetic groups and the congruence problem, Russian Academy of Sciences. Izvestiya. Mathematics 40 (1993), 455-476.
17. [PR94] V. Platonov and A. Rapinchuk, Algebraic Groups and Number Theory, Pure and Applied Mathematics, Vol. 139, Academic Press, Boston, MA, 1994.
18. [PR96] G. Prasad and A. S. Rapinchuk, Computation of the metaplectic kernel, Publications Mathématiques de l'Institut des Hautes Études Scientifiques 84 (1996), 91-187.
19. [Pra77] G. Prasad, Strong approximation for semi-simple groups over function fields, Annals of Mathematics 105 (1977), 553-572.
20. [Rag76] M. S. Raghunathan, On the congruence subgroup problem, Publications Mathématiques de l'Institut des Hautes Études Scientifiques 46 (1976), 107-161.
21. [Ros02] M. Rosen, Number Theory in Function Fields, Graduate Texts in Mathematics, Vol. 210, Springer-Verlag, New York, 2002.
22. [Seg99] Y. Segev, On finite homomorphic images of the multiplicative group of a division algebra, Annals of Mathematics 140 (1999), 219-251.
23. [Ser70] J.-P. Serre, Le problème des groupes de congruence pour SL 2, Annals of Mathematics 92 (1970), 489-527.
24. [Ser92] J.-P. Serre, Lie Algebras and Lie Groups, second edn., Lecture Notes in Mathematics, Vol. 1500, Springer-Verlag, Berlin, 1992.
25. [Ven88] T. N. Venkataramana, On superrigidity and arithmeticity of lattices in semisimple groups over local fields of arbitrary characteristic, Inventiones Mathematicae 92 (1988), 255-306.