Representation theory of towers of recollement: Theory, notes, and examples

Journal of Algebra

Volumn 302, Issue 1, 2006, Pages 340-360

  Cox, Anton ^a   Martin, Paul ^a   Parker, Alison ^b   Xi, Changchang ^c  

^a CITY UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF LEICESTER   (United Kingdom)

^c BEIJING NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646800904     PISSN: 00218693     EISSN: 1090266X     Source Type: Journal    
DOI: 10.1016/j.jalgebra.2006.01.009     Document Type: Article

References (38)

1. Beilinson A.A., Bernstein J.N., and Deligne P. Faisceaux pervers. Astérisque 100 (1982) 5-171
2. Bloss M. G-Colored partition algebras as centralizer algebras of wreath products. J. Algebra 256 (2003) 690-710
3. Brauer R. On algebras which are connected with the semisimple continuous groups. Ann. of Math. 38 (1937) 857-872
4. Brown W. An algebra related to the orthogonal group. Michigan Math. J. 3 (1955) 1-22
5. Cline E., Parshall B., and Scott L. Finite-dimensional algebras and highest weight categories. J. Reine Angew. Math. 391 (1988) 85-99
6. Cline E., Parshall B., and Scott L. Stratifying endomorphism algebras. Mem. Amer. Math. Soc. 124 (1996)
7. A.G. Cox, M.D. Visscher, P.P. Martin, The blocks of the Brauer algebra in characteristic zero, preprint
8. Cox A.G., Graham J.J., and Martin P.P. The blob algebra in positive characteristic. J. Algebra 266 (2003) 584-635
9. Dlab V. Properly stratified algebras. C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 191-196
10. Dlab V., and Ringel C.M. Quasi-hereditary algebras. Illinois J. Math. 33 (1989) 280-291
11. Donkin S. The q-Schur Algebra. London Math. Soc. Lecture Note Ser. vol. 253 (1998), Cambridge Univ. Press
12. Doran W.F., Wales D.B., and Hanlon P.J. On the semisimplicity of the Brauer centralizer algebras. J. Algebra 211 (1999) 647-685
13. Goodman F.M., de la Harpe P., and Jones V.F.R. Coxeter Graphs and Towers of Algebras. Math. Sci. Res. Inst. Publ. vol. 14 (1989), Springer-Verlag
14. F.M. Goodman, H. Hauschild, Affine Birman-Wenzl-Murakami algebras and tangles in the solid torus, preprint
15. Graham J.J., and Lehrer G.I. Cellular algebras. Invent. Math. 123 (1996) 1-34
16. n. Lecture Notes in Math. vol. 830 (1980), Springer-Verlag
17. Green R.M. Generalized Temperley-Lieb algebras and decorated tangles. J. Knot Theory Ramifications 7 (1998) 155-171
18. Green R.M. Tabular algebras and their asymptotic versions. J. Algebra 252 (2002) 27-64
19. Jantzen J.C. Representations of Algebraic Groups. Math. Surveys Monogr. second ed. vol. 107 (2003), Amer. Math. Soc.
20. Jones V.F.R. Index for subfactors. Invent. Math. 72 (1983) 1-25
21. V.F.R. Jones, Planar algebras I, preprint, 1997
22. König S., and Xi C. On the structure of cellular algebras. Algebras and Modules, II. Geiranger, 1996. CMS Conf. Proc. vol. 24 (1998), Amer. Math. Soc. 365-386
23. Martin P.P. Potts Models and Related Problems in Statistical Mechanics (1991), World Scientific, Singapore
24. Martin P.P. Temperley-Lieb algebras for nonplanar statistical mechanics-the partition algebra. J. Knot Theory Ramifications 3 (1994) 51-82 originally appeared as preprint YCTP-P34-92 in 1992
25. Martin P.P. The partition algebra and the Potts model transfer matrix spectrum in high dimensions. J. Phys. A 33 (2000) 3669-3695
26. P.P. Martin, M. Alvarez, R.M. Green, A.E. Parker, Towers of recollement and bases for diagram algebras: Planar diagrams and a little beyond, preprint
27. Martin P.P., and Elgamal A. Ramified partition algebras. Math. Z. 246 (2004) 473-500
28. Martin P.P., and Ryom-Hansen S. Virtual algebraic Lie theory: Tilting modules and Ringel duals for blob algebras. Proc. London Math. Soc. 89 (2004) 655-675
29. Martin P.P., and Saleur H. The blob algebra and the periodic Temperley-Lieb algebra. Lett. Math. Phys. 30 (1994) 189-206
30. Martin P.P., and Woodcock D. On the structure of the blob algebra. J. Algebra 225 (2000) 957-988
31. Martin P.P., Woodcock D., and Levy D. A diagrammatic approach to Hecke algebras of the reflection equation. J. Phys. A 33 (2000) 1265-1296
32. Martin S. Schur Algebras and Representation Theory (1993), Cambridge Univ. Press
33. Mazorchuk V. On the structure of Brauer semigroup and its partial analogue. Problems in Algebra 13 (1998) 29-45
34. n. Comm. Algebra 30 (2002) 3489-3513
35. Rui H. A criterion on the semisimple Brauer algebras. J. Combin. Theory Ser. A 111 (2005) 78-88
36. Rui H., and Xi C. The representation theory of cyclotomic Temperley-Lieb algebras. Comment. Math. Helv. 79 (2004) 427-450
37. Vershik A.M., and Okun'kov A.Y. An inductive method of expounding the representation theory of symmetric groups. Russian Math. Surveys 51 (1996) 355-356
38. Wenzl H. On the structure of Brauer's centralizer algebra. Ann. of Math. (2) 128 (1988) 173-193