On the semisimplicity of the Brauer centralizer algebras

Journal of Algebra

Volumn 211, Issue 2, 1999, Pages 647-685

  Doran IV, William F ^a   Wales, David B ^a   Hanlon, Philip J ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033555084     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.1998.7592     Document Type: Article

References (16)

1. [Br] R. Brauer, On algebras which are connected with the semisimple continuous groups, Math. 38 (1937), 857-872.
2. [Brn] W. Brown, An algebra related to the orthogonal group, Michigan Math. J. 3 (1955-1956), 1-22.
3. [D] P. Diaconis, "Group Representations in Probability and Statistics," Institute of Mathematical Statistics Lecture Notes, Monograph Series 11.
4. [GL] J. J. Graham and G. I. Leher, Cellular algebras, Invent. Math. 123 (1996), 1-34.
5. n," Springer-Verlag, Berlin, 1980.
6. [HW1] P. Hanlon and D. Wales, On the decomposition of Brauer's centralizer algebras, J. Algebra 121 (1989), 409-445.
7. [HW2] P. Hanlon and D. Wales, Eigenvalues connected with Brauer's centralizer algebras, J. Algebra 121 (1989), 446-476.
8. [HW3] P. Hanlon and D. Wales, Computing the discriminants of Brauer's centralizer algebras, Math. Comp. 54 (1990), 771-796.
9. [HW4] P. Hanlon and D. Wales, A tower construction for the radical in Brauer's centralizer algebras, J. Algebra 164 (1994), 773-830.
10. [J] G. James, "The Representation Theory of the Symmetric Group," Lecture Notes in Mathematics 682, Springer-Verlag, Berlin, 1978.
11. [JK] G. James and A. Kerber, The representation theory of the symmetric group, in "Encyclopedia of Mathematics and Its Applications" (G.-C. Rota, Ed.), Addison-Wesley, Reading, MA, 1981.
12. [M] P. Martin, The structure of the partition algebras, J. Algebra 183 (1996), 319-358.
13. [N] M. Nazarov, Young's orthogonal form for Brauer's centralizer algebra, J. Algebra 182 (1996), 664-693.
14. [S] B. Sagan, "The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions," Wadsworth and Brooks/Cole, Pacific Grove, CA, 1991.
15. [Wen] H. Wenzl, On the structure of Brauer's centralizer algebras, Ann. Math. 128 (1988), 173-193.
16. [Wey] H. Weyl, "The Classical Groups," Princeton Univ. Press, Princeton, NJ, 1939.