Abstract
The Brauer semigroup replaces the group ring of the symmetric group in the study of of the commutant of tensor powers of representations of classical groups of the series Bn, Cn, Dn. In this paper an elementary description of their irreducible representations is given.
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Literature cited
R. Brauer, “On algebras which are connected with semisimple continuous groups,” Ann. Math.,38, No. 4, 857–872 (1937).
J. S. Birman and H. Wenzl, “Braids, link polynomials and a new algebra,” Preprint, 1987.
H. Wenzl, “On the structure of Brauer's centralizer algebras,” Preprint, 1987.
A. A. Klyachko, “Centralizers of involutions and models of the symmetric and general linear groups,” in: Studies in Number Theory [in Russian], Vol. 7, Saratov (1987), pp. 59–64.
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institute im. V. A. Steklova AN SSSR, Vol. 164, pp. 189–193, 1987.
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Kerov, S.V. Realizations of representations of the Brauer semigroup. J Math Sci 47, 2503–2507 (1989). https://doi.org/10.1007/BF01840432
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DOI: https://doi.org/10.1007/BF01840432