Journal of the Ramanujan Mathematical Society
Volume 29, Issue 3, September 2014 pp. 273–294.
Semisimplicity of even Brauer algebras
Authors:
Anuradha Nebhani
Author institution:Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, Maharashtra, India
Summary:
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
SO(2n). This algebra, denoted by Dr(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
Dr(2n) is not associative, we study the semisimplicity of the
largest associative quotient of Dr(2n), denoted by
Dr(2n). In this paper, we study the even Brauer
algebra Dr(2) and find a chain of its
two-sided ideals. Finally we prove that D1(2),
D2(2) and D3(2) are semisimple
algebras over C.
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