IJPAM: Volume 100, No. 2 (2015)
ALGEBRAS OF THE MIXED TENSOR REPRESENTATION
OF LIE SUPERALGEBRAS
Ramanujan Institute for Advanced study in Mathematics
University of Madras
Chepauk, Chennai, 600 005, Tamilnadu, INDIA
Abstract. In this paper, we prove that the walled signed Brauer algebra is embedded in a canonical fashion as a subalgebra of a walled Brauer algebra and the walled signed Brauer algebra is the centralizer algebra of in the walled Brauer algebra Finally we prove that, if the walled signed Brauer algebra is isomorphic to the centralizer algebra of the - action on the mixed tensor space where is the complex general linear Lie superalgebra, is the natural representation of and is the dual of
Received: September 14, 2014
AMS Subject Classification: 17B10
Key Words and Phrases: walled Brauer algebra, signed Brauer algebra, Lie superalgebra
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DOI: 10.12732/ijpam.v100i2.6 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 235 -