Characters of Brauer's centralizer algebras.
Arun Ram
Source: Pacific J. Math. Volume 169, Number 1 (1995), 173-200.
Primary Subjects: 20C30
Secondary Subjects: 20G05
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102620457
Zentralblatt MATH identifier:
0839.20019
Mathematical Reviews number (MathSciNet):
MR1346252
References
[Bou] N. Bourbaki, Groupes et Algebres de Lie, Chap. 4-6. Paris: Hermann 1960.
Mathematical Reviews (MathSciNet):
MR24:A2641
[Br] R. Brauer, On algebras which are connected with the semisimple contin- uous groups, Ann. Math., 38 (1937), 854-872.
Mathematical Reviews (MathSciNet):
MR1503378
Zentralblatt MATH:
0017.39105
[Pr] F.G. Probenius, Uberdie Charactere der symmetschen Gruppe, Sitzungs- berichte der Koniglich Preussischen Akademie der Wissenschaften zu Berlin (1900), 516-534; reprinted in Gessamelte Abhandlungen 3, 148- 166.
[HW1] P. Hanlon and D.B. Wales, On the decomposition of Brauer's centralizer algebras, J. Algebra, 121 (1989),409-445.
Mathematical Reviews (MathSciNet):
MR91a:20041a
Zentralblatt MATH:
0695.20026
[HW2] P. Hanlon and D.B. Wales, Eigenvalues connected with Brauer's centralizer algebras, J. Al- gebra, 121 (1989), 446-476.
Mathematical Reviews (MathSciNet):
MR91a:20041b
Zentralblatt MATH:
0695.20027
[Ji] M. Jimbo, A q-analogue ofU($l(N + 1)), Hecke algebra, and the Yang- Baxter equation, Lett. Math. Phys., 11 (1986), 247-252.
Mathematical Reviews (MathSciNet):
MR87k:17011
Zentralblatt MATH:
0602.17005
[KT] K. Koike and I. Terada, Young diagrammatic methods for the represen- tation theory of the classical groups of type Bn, Cn, Dn, J. Algebra, 107 (1987), 466-511.
Mathematical Reviews (MathSciNet):
MR88i:22035
Zentralblatt MATH:
0622.20033
[Li] D.E.Littlewood, Theory of Group Characters, Oxford University Press, (1940).
Mathematical Reviews (MathSciNet):
MR2:3a
Zentralblatt MATH:
0025.00901
[Mac] I.G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford (1979).
Mathematical Reviews (MathSciNet):
MR84g:05003
Zentralblatt MATH:
0487.20007
[Pr] R. Proctor, Interconnections between symplectic and orthogonal charac- ters, Contemp. Math., 88 (1989), 145-162.
Mathematical Reviews (MathSciNet):
MR90h:22017
Zentralblatt MATH:
0697.22020
[Rl] A. Ram, A frobenius formula for the characters of the Hecke algebras, Invent. Math., 106 (1991), 461-488.
Mathematical Reviews (MathSciNet):
MR93c:20029
Zentralblatt MATH:
0758.05099
[R2] A. Ram, Representation theory and character theory of centralizer alge- bras, Dissertation, University of California, San Diego, 1991.
[Scl] I. Schur, Uber eine Klasse von Matrizen, die sich einer gegeben Matrix zuordnen lassen, Dissertation, 1901;reprinted in Gessamelte Abhandlun- gen 1, 1-72.
[Sc2] I. Schur, Uber die rationalen Darstellungen der allgemeinen linearen Gruppe, Sitzungsberichte der Koniglich Preussischen Akademie der
[St] R. Stanley, Letter to Phil Hanlon, 1985.
[Ste] J. Stembridge, unpublished notes, 1987.
[Wy] H. Weyl, ClassicalGroups, Princeton University Press, 1946.
Mathematical Reviews (MathSciNet):
MR98k:01049
[Wzl] H. Wenzl, On the structure of Brauer's centralizer algebras,Ann. of Math., 128 (1988), 173-193.
Mathematical Reviews (MathSciNet):
MR89h:20059
Zentralblatt MATH:
0656.20040
[Wz2] H. Wenzl, Quantum groups and subfactors of type B, C and D, Comm. Math. Phys., 133 (1990), 1-49.
Mathematical Reviews (MathSciNet):
MR92k:17032
Zentralblatt MATH:
0744.17021
Pacific Journal of Mathematics