On the semisimplicity of cyclotomic temperley-lieb algebras

Michigan Mathematical Journal

Volumn 53, Issue 1, 2005, Pages 83-96

  Rui, Hebing ^a   Xi, Changchang ^b   Yu, Weihua ^a  

^a EAST CHINA NORMAL UNIVERSITY   (China)

^b BEIJING NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18844452626     PISSN: 00262285     EISSN: None     Source Type: Journal    
DOI: 10.1307/mmj/1114021086     Document Type: Article

References (16)

1. A. Cox, J. Graham, and P. Martin, The blob algebra in positive characteristic, J. Algebra 266 (2003), 584-635.
2. W. Doran, D. Wales, and P. Hanlon, On the semisimplicity of the Brauer centraliser algebras, J. Algebra 211 (1999), 647-685.
3. J. Graham and G. Lehrer, Cellular algebras, Invent. Math. 123 (1996), 1-34.
4. _, The representation theory of affine Temperley-Lieb algebras, Enseign. Math. (2) 44 (1998), 173-218.
5. _, The two-step nilpotent representations of the extended affine Hecke algebra of type A, Compositio Math. 133 (2002), 173-197.
6. _, Diagram algebras, Hecke algebras and decomposition numbers at roots of unity, Ann. Sci. École Norm. Sup. (5) 36 (2003), 479-524.
7. n, Lecture Notes in Math., 830, Springer-Verlag, New York, 1980.
8. R. M. Green, On representations of affine Temperley-Lieb algebras, Algebras and modules, II (Geiranger, 1996), CMS Conf. Proc., 24, pp. 245-261, Amer. Math. Soc., Providence, RI, 1998.
9. V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. (2) 126 (1987), 335-388.
10. S. König and C. C. Xi, On the structure of cellular algebras, Algebras and modules, II (Geiranger, 1996), CMS Conf. Proc., 24, pp. 365-386, Amer. Math. Soc., Providence, RI, 1998.
11. P. Martin, The structure of the partition algebras, J. Algebra 183 (1996), 319-358.
12. P. Martin and H. Saleur, The blob algebra and the periodic Temperley-Lieb algebra, Lett. Math. Phys. 30 (1994), 189-206.
13. H. Rui and C. C. Xi, The representations of the cyclotomic Temperley-Lieb algebras, Comment. Math. Helv. 79 (2004), 427-450.
14. H. Rui and W. Yu, On the semisimplicity of the cyclotomic Brauer algebras, J. Algebra 277 (2004), 187-221.
15. H. N. V. Temperley and E. H. Lieb, Relations between percolation and colouring problems and other graph theoretical problems associated with regular planar lattices: Some exact results for the precolation problem, Proc. Roy. Soc. London Ser. A 322 (1971), 251-273.
16. B. W. Westbury, The representation theory of the Temperley-Lieb algebras, Math. Z. 219 (1995), 539-565.