Young's orthogonal form for Brauer's centralizer algebra

Journal of Algebra

Volumn 182, Issue 3, 1996, Pages 664-693

  Nazarov, Maxim ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030585662     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.1996.0195     Document Type: Article

References (25)

1. [Br] R. Brauer, On algebras which are connected with the semisimple continuous groups, Ann. of Math. 38 (1937), 857-872.
2. [BW] J. S. Birman and H. Wenzl, Braids, link polynomials and a new algebra, Trans. Amer. Math. Soc. 313 (1989), 249-273.
3. [B1] W. P. Brown, An algebra related to the orthogonal group, Michigan Math. J. 3 (1955-1956), 1-22.
4. f Ann. of Math. 63 (1956), 324-335.
5. [C1] I. V. Cherednik, On special bases of irreducible finite-dimensional representations of the degenerate affine Hecke algebra, Functional Anal. Appl. 20 (1986), 76-78.
6. [C2] I. V. Cherednik, A unification of Knizhnik-Zamolodchikov and Dunkl operators via affine Hecke algebras, Invent. Math. 106 (1991), 411-431.
7. [D] V. G. Drinfeld, Degenerate affine Hecke algebras and Yangians, Functional Anal. Appl. 20 (1986), 56-58.
8. [EK] N. El Samra and R. C. King, Dimensions of irreducible representations of the classical Lie groups, J. Phys. A 12 (1979), 2317-2328.
9. [HW] P. Hanlon and D. Wales, A tower construction for the radical in Brauer's centralizer algebras, J. Algebra 164 (1994), 773-830.
10. [JMO] M. Jimbo, T. Miwa, and M. Okado, Solvable lattice models related to the vector representations of the classical Lie algebras, Comm. Math. Phys. 116 (1988), 507-525.
11. [Ju] A.-A. A. Jucys, Symmetric polynomials and the center of the symmetric group ring, Rep. Math. Phys. 5 (1974), 107-112.
12. [Ke] S. V. Kerov, Realization of representations of the Brauer semigroup, J. Soviet Math. 47 (1989), 2503-2507.
13. [Ki] R. C. King, Modification rules and products of irreducible representations of the unitary, orthogonal, and symplectic groups, J. Math. Phys. 12 (1971), 1588-1598.
14. [L] D. E. Littlewood, Products and plethysms of characters with orthogonal, symplectic and symmetric groups, Canad. J. Math. 10 (1958), 17-32.
15. [Ma] I. G. Macdonald, "Symmetric Functions and Hall Polynomials," Clarendon Press, Oxford, 1979.
16. [Mk] J. Murakami, The representations of the q-analogue of Brauer's centralizer algebras and the Kauffman polynomial of links, Publ. Res. Inst. Math. Sci. 26 (1990), 935-945.
17. [Mo] V. F. Molchanov, On matrix elements of irreducible representations of a symmetric group, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1 (1966), 52-57.
18. [Mp] G. E. Murphy, A new construction of Young's seminormal representation of the symmetric group, J. Algebra 69 (1981), 287-291.
19. [O] G. I. Olshanskiǐ, Representations of infinite-dimensional classical groups, limits of enveloping algebras, and Yangians, in "Topics in Representation Theory," pp. 1-66, Adv. Soviet Math., Vol. 2, Amer. Math. Soc., Providence, RI, 1991.
20. [RW] A. Ram and H. Wenzl, Matrix units for centralizer algebras, J. Algebra 145 (1992), 378-395.
21. [V1] A. M. Vershik, Local algebras and a new version of Young's orthogonal form, in "Topics in Algebra," pp. 467-473, Banach Center Publications, Vol. 26, Polish Scientific, Warsaw, 1990.
22. [V2] A. M. Vershik, Local stationary algebras, Amer. Math. Soc. Transl. 148 (1991), 1-13.
23. [W] H. Wenzl, On the structure of Brauer's centralizer algebras, Ann. of Math. 128 (1988), 173-193.
24. [Wy] H. Weyl, "Classical Groups, Their Invariants and Representations," Princeton Univ. Press, Princeton, NJ, 1946.
25. [Y] A. Young, On quantitative substitutional analysis, VI, Proc. London Math. Soc. 31 (1931), 253-289.