46 research outputs found
Schur-Weyl duality for the Brauer algebra and the ortho-symplectic Lie superalgebra
We give a proof of a Schur-Weyl duality statement between the Brauer algebra
and the ortho-symplectic Lie superalgebra .Comment: 22 pages, minor changes, to appear in M
On the radical of Brauer algebras
The radical of the Brauer algebra B_f^x is known to be non-trivial when the
parameter x is an integer subject to certain conditions (with respect to f). In
these cases, we display a wide family of elements in the radical, which are
explicitly described by means of the diagrams of the usual basis of B_f^x . The
proof is by direct approach for x=0, and via classical Invariant Theory in the
other cases, exploiting then the well-known representation of Brauer algebras
as centralizer algebras of orthogonal or symplectic groups acting on tensor
powers of their standard representation. This also gives a great part of the
radical of the generic indecomposable B_f^x-modules. We conjecture that this
part is indeed the whole radical in the case of modules, and it is the whole
part in a suitable step of the standard filtration in the case of the algebra.
As an application, we find some more precise results for the module of
pointed chord diagrams, and for the Temperley-Lieb algebra - realised inside
B_f^1 - acting on it.Comment: AMS-TeX file, 2 figures (in EPS format), 25 pages. This is the final
version, to appear in "Mathematische Zeitschrift". Comparing to the previous
one, it has been streamlined and shortened - yet the mathematical content
stands the same. The list of references has been update
The Jucys-Murphy basis and semisimplicty criteria for the -Brauer algebra
We construct the Jucys-Murphy elements and the Jucys-Murphy basis for the
-Brauer algebra in the sense of Mathas[11]. We also give a necessary and
sufficient condition for the -Brauer algebra being (split) semisimple over
an arbitrary field.Comment: 21 page