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Semisimplicity of even Brauer algebras

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Title Semisimplicity of even Brauer algebras
 
Creator NEBHANI, A
 
Subject CENTRALIZER ALGEBRAS
 
Description In 1937, Richard Brauer introduced certain diagram algebras corresponding to the centralizer algebra of transformations commuting with the action of the complex special orthogonal group S O(2n). This algebra, denoted by D-r(2n), is called the even Brauer algebra. The even Brauer algebra plays the same role for the special orthogonal group that the symmetric group algebra does for the representation theory of the general linear group in Schur-Weyl duality. Studying the semisimplicity of the even Brauer algebra is useful in studying the representations of the special orthogonal groups. Since the even Brauer algebra D-r(2n) is not associative, we study the semisimplicity of the largest associative quotient of D-r(2n), denoted by . In this paper, we study the even Brauer algebra and find a chain of its two-sided ideals. Finally we prove that , and are semisimple algebras over C.
 
Publisher RAMANUJAN MATHEMATICAL SOC
 
Date 2014-12-29T04:56:49Z
2014-12-29T04:56:49Z
2014
 
Type Article
 
Identifier JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY, 29(3)273-294
0970-1249
2320-3110
http://dspace.library.iitb.ac.in/jspui/handle/100/17132
 
Language English