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Abstract: One of the most beautiful results in mathematics
is the Schur-Weyl duality between the general linear group and the
symmetric group. This result brings together the representation theory
of these two groups by studying their action on tensor space.
In this talk I will discuss a way to obtain tensor representations of
the Hecke algebra of type~B and of the BMW algebra of type B. Using
these representations one can show that there is a duality between the
quantum group related to the special linear algebra and the Hecke
algebra of type B; and a duality between the quantum group related to
the special orthogonal algebra and the type~B BMW algebra. I will
define all the algebras mentioned in this abstract and focus on the
combinatorics of the problem.
Part of this talk is joint work with H. Wenzl.
This talk will be accessible to graduate students.
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