Cyclotomic Temperley–Lieb Algebra of Type D and Its Representation Theory

REFERENCES

• Ariki , S. , Koike , K. ( 1994 ). A Hecke algebra of (ℤ/rℤ)≀𝔖 n and construction of its irreducible representations . Adv. Math. 106 : 216 – 243 .
   Web of Science ®Google Scholar
• Cao , Y. Z. ( 2003 ). On the quasi-heredity and the semi-simplicity of cellular algebras . J. Algebra 267 : 323 – 341 .
   Web of Science ®Google Scholar
• Cao , Y. Z. , Zhu , P. ( 2006 ). Cyclotomic blob algebras and its representation theory . J. Pure and Applied Algebra 204 : 666 – 695 .
   Google Scholar
• Cline , E. , Parshall , B. J. , Scott , L. L. ( 1988 ). Finite dimensional algebras and highest weight categories . J. Reine Angew. Math. 391 : 85 – 99 .
   Web of Science ®Google Scholar
• Fan , C. K. , Green , R. M. ( 1999 ). On the affine Temperley–Lieb algebras . J. London Math. Soc. 60 : 366 – 380 .
   Google Scholar
• Freyd , P. J. , Yetter , D. N. ( 1989 ). Braided compact closed categories with applications to low dimensional topology . Adv. Math. 77 : 156 – 182 .
   Web of Science ®Google Scholar
• Graham , J. ( 1995 ). Modular Representations of Hecke Algebras and Related Algebras. Ph.D. thesis, University of Sydney .
   Google Scholar
• Graham , J. , Lehrer , G. (1996). Cellular algebras. Invent. Math. 123:1–34.
   Web of Science ®Google Scholar
• Graham , J. , Lehrer , G. ( 1998 ). The representation theory of affine Temperley–Lieb algebras . L'Enseignment Math. 44 : 173 – 218 .
   Google Scholar
• Green , R. M. ( 1998 ). Generalized Temperley–Lieb algebras and decorated tangles . J. Knot. Theory Ramifications 7 : 155 – 171 .
   Web of Science ®Google Scholar
• Jones , V. F. R. ( 1983 ). Index for subfactors . Invent. Math. 72 : 1 – 25 .
   Web of Science ®Google Scholar
• Jones , V. F. R. ( 1987 ). Hecke algebra representations of braid groups and link polynomials . Ann. of Math. 126 ( 2 ): 335 – 388 .
   Web of Science ®Google Scholar
• Kauffman , L. H. ( 1990 ). An invariant of regular isotopy . Trans. Amer. Math. Soc. 318 : 417 – 471 .
   Web of Science ®Google Scholar
• König , S. , Wang , J. C. ( 2008 ). Cyclotomic extensions of diagram algebras . Comm. Algebra 36 ( 5 ): 1739 – 1757 .
   Google Scholar
• König , S. , Xi , C. C. ( 1998 ). On the structure of cellular algebras . In: Reiten , I. , Smalø , S. , Solberg , Ø. , eds. Algebras and Modules II Canadian Mathematical Society Conference Proceedings 24 : 365 – 386 .
   Google Scholar
• König , S. , Xi , C. C. ( 1999 ). When is a cellular algebra quasi-hereditary? . Math. Ann. 315 : 281 – 293 .
   Web of Science ®Google Scholar
• König , S. , Xi , C. C. ( 1999 ). On the number of cells of a cellular algebra . Comm. Algebra 27 : 5463 – 5470 .
   Web of Science ®Google Scholar
• König S. , Xi , C. C. ( 1999 ). Cellular algebras and quasi-hereditary algebras: a comparison . Electron. Res. Announc. Amer. Math. Soc. 5 : 71 – 75 .
   Google Scholar
• König S., Xi , C. C. ( 2001 ). A characteristic free approach to Brauer algebras . Trans. Amer. Math. Soc. 353 : 1489 – 1505 .
   Google Scholar
• Martin , P. P. , Saleur , H. ( 1994 ). The blob algebra and the periodic Temperley–Lieb algebra . Lett. Math. Phys. 30 : 189 – 206 .
   Web of Science ®Google Scholar
• Rui , H. B. , Xi , C. C. ( 2004 ). The representation theory of cyclotomic Temperley–Lieb algebras . Comment. Math. Helv. 79 ( 2 ): 427 – 450 .
   Web of Science ®Google Scholar
• Rui , H. B. , Xi , C. C. , Yu , W. H. ( 2005 ). On the semi-simplicity of cyclotomic Temperley–Lieb algebras . Michigan Math. J. 53 ( 1 ): 83 – 96 .
   Google Scholar
• Temperley , H. N. V. , Lieb , E. H. ( 1971 ). Relations between percolation and coloring problems and other graph theoretical problems associated with regular planar lattices: some exact results for the percolation problem . Proc. Roy. Soc. London Ser. A 322 : 251 – 280 .
   Web of Science ®Google Scholar
• Westbury , B. W. ( 1995 ). The representation theory of the Temperley–Lieb algebra . Math. Z. 219 : 539 – 565 .
   Google Scholar
• Xi , C. C. ( 1999 ). Partition algebras are cellular . Compos. Math. 119 : 99 – 109 .
   Web of Science ®Google Scholar
• Xi , C. C. ( 2000 ). On the quasi-heredity of Birman–Wenzl algebras . Adv. Math. 154 : 280 – 298 .
   Web of Science ®Google Scholar
• Xi , C. C. ( 2002 ). Standardly stratified algebras and cellular algebras . Math. Proc. Cambridge Philos. Soc. 133 : 37 – 53 .
   Web of Science ®Google Scholar
• Present address: Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1 N GN5. [email protected]
   Google Scholar
• Communicated by D. Happel.
   Google Scholar