|
The independence of characters on non-abelian groups
Author(s):
David
Grow;
Kathryn
E.
Hare
Journal:
Proc. Amer. Math. Soc.
132
(2004),
3641-3651.
MSC (2000):
Primary 43A65;
Secondary 43A46, 22E46
Posted:
May 20, 2004
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We show that there are characters of compact, connected, non-abelian groups that approximate random choices of signs. The work was motivated by Kronecker's theorem on the independence of exponential functions and has applications to thin sets.
References:
- 1.
- H. Bohr, Zur Theorie der Fast Periodischen Funktionen (I. Teil), Acta Math. 45 (1925), 29-127.
- 2.
- H. Bohr, Almost periodic functions (Translated by H. Cohn), Chelsea Publishing Co., New York, 1947. MR 8:512a
- 3.
- T. Bröcker and T. tom Dieck, Representations of compact Lie groups, Graduate Texts in Mathematics, no. 98, Springer-Verlag, New York, 1985. MR 86i:22023
- 4.
- T. Dooley, Central lacunary sets for Lie groups, J. Austral. Math. Soc. Ser. A 45 (1988), 30-45. MR 89j:43007
- 5.
- P. Gallagher, Zeroes of group characters, Math. Z. 87 (1965), 363-364. MR 31:276
- 6.
- K. Hare, The size of characters of compact Lie groups, Studia Mathematica 129 (1998), 1-18. MR 99c:43013
- 7.
- K. Hare, Central Sidonicity for compact Lie groups, Ann. Inst. Fourier (Grenoble) 45 (1995), 547-564. MR 96i:43004
- 8.
- K. Hare and D. Wilson, Weighted
 -Sidon sets, J. Austral. Math. Soc. Ser. A 61 (1996), 73-95.MR 97j:43002 - 9.
- S. Hartman and C. Ryll-Nardzewski, Almost periodic extensions of functions, Colloq. Math. 12 (1964), 23-39.MR 29:5057
- 10.
- E. Hewitt and K. Ross, Abstract harmonic analysis II, Springer-Verlag, New York, 1970. MR 41:7378
- 11.
- E. Hewitt and H. Zuckerman, A group theoretic method in approximation theory, Annals of Mathematics 52 (1950), 557-567. MR 12:801c
- 12.
- J. Humphreys, Introduction to Lie algebras and representation theory, Springer-Verlag, New York, 1972. MR 48:2197
- 13.
- J. Lopez and K. Ross, Sidon sets, Lecture Notes in Pure and Applied Math. 13, Marcel Dekker, New York, 1975. MR 55:13173
- 14.
- W. Parker, Central Sidon and central
 sets, J. Austral. Math. Soc. 14 (1972), 62-74. MR 47:9178 - 15.
- J. Price, Lie groups and compact groups, London Math. Soc. Lecture Note Series No. 25, Cambridge Univ. Press, Cambridge, 1977. MR 56:8743
- 16.
- D. Ragozin, Central measures on compact simple Lie groups, J. Funct. Anal. 10 (1972), 212-229. MR 49:5715
- 17.
- L. T. Ramsey, Comparisons of Sidon and
 sets, Colloq. Math. 70 (1996), 103-132. MR 97m:43004 - 18.
- D. Rider, Central lacunary sets, Monatsh. Math. 76 (1972), 328-338. MR 51:3801
- 19.
- W. Rudin, Fourier analysis on groups, Interscience Publishers, New York, 1962. MR 27:2808
- 20.
- B. Simon, Representations of finite and compact groups, Graduate Studies in Mathematics 10, Amer. Math. Soc., Providence, RI, 1996. MR 97c:22001
- 21.
- V. Varadarajan, Lie groups, Lie algebras and their representations, Springer-Verlag, New York, 1984. MR 85e:22001
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
43A65,
43A46, 22E46
Retrieve articles in all Journals with MSC
(2000):
43A65,
43A46, 22E46
Additional Information:
David
Grow
Affiliation:
Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, Missouri 65409
Email:
grow@umr.edu
Kathryn
E.
Hare
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email:
kehare@uwaterloo.ca
DOI:
10.1090/S0002-9939-04-07506-9
PII:
S 0002-9939(04)07506-9
Keywords:
Characters,
independence,
compact non-abelian groups,
compact Lie groups
Received by editor(s):
August 22, 2003
Posted:
May 20, 2004
Additional Notes:
This research was supported in part by NSERC and the Swedish Natural Sciences Research Council
Communicated by:
Andreas Seeger
Copyright of article:
Copyright
2004,
American Mathematical Society
|
Comments: webmaster@ams.org