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Brauer algebras were introduced by Richard Brauer in order
to study the tensor representations of the defining space
for orthogonal or symplectic groups. In 1995, Graham and
Lehrer proved that Brauer algebras over a commutative ring
are cellular algebras. A natural question is how to compute
the Gram determinant for each cell module of a Brauer algebra.
In this talk, I will answer this question by giving a
recursive formula. Such a formula has been generalized to
Birman-Wenzl algebras, the q-analogue of Brauer algebras. We
also give necessary and sufficient conditions for the
semisimplicity of Birman-Wenzl algebras over an arbitrary
field, which improves work by H. Wenzl in 1990.
This is joint work with Mei Si. After the seminar we will take the speaker to lunch. See the Algebra Seminar web page for information about other seminars in the series. Anthony Henderson anthonyh@maths.usyd.edu.au. |