On the Blocks of the Walled Brauer Algebra
نویسنده
چکیده
We determine the blocks of the walled Brauer algebra in characteristic zero. These can be described in terms of orbits of the action of a Weyl group of type A on a certain set of weights. In positive characteristic we give a linkage principle in terms of orbits of the corresponding affine Weyl group. We also classify the semisimple walled Brauer algebras in all characteristics.
منابع مشابه
Traces on Infinite - Dimensional Brauer Algebras ∗
We describe the central measures for the random walk on graded graphs. Using this description , we obtain the list of all finite traces on three infinite-dimensional algebras: on the Brauer algebra, on the partition algebra, and on the walled Brauer algebra. For the first two algebras, these lists coincide with the list of all finite traces of the infinite symmetric group. For the walled Brauer...
متن کاملThe Blocks of the Brauer Algebra in Characteristic Zero
We determine the blocks of the Brauer algebra in characteristic zero. We also give information on the submodule structure of standard modules for this algebra.
متن کاملQuantum Walled Brauer-clifford Superalgebras
We introduce a new family of superalgebras, the quantum walled Brauer-Clifford superalgebras BCr,s(q). The superalgebra BCr,s(q) is a quantum deformation of the walled BrauerClifford superalgebra BCr,s and a super version of the quantum walled Brauer algebra. We prove that BCr,s(q) is the centralizer superalgebra of the action of Uq(q(n)) on the mixed tensor space V q = V ⊗r q ⊗ (V∗ q) when n ≥...
متن کاملQuantized mixed tensor space and Schur–Weyl duality I
This paper studies a q-deformation, Br,s(q), of the walled Brauer algebra (a certain subalgebra of the Brauer algebra) and shows that the centralizer algebra for the action of the quantum group UR(gln) on mixed tensor space (R) ⊗ (Rn)∗ is generated by the action of Br,s(q) for any commutative ring R with one and an invertible element q.
متن کاملQuantized mixed tensor space and Schur – Weyl duality
Generically (for r + s ≥ n) the centralizer algebra for the action of GLn(C) on mixed tensor space (C n) ⊗r ⊗ ((C n) *) ⊗s is a certain subalgebra of the Brauer algebra, known as the walled (or rational) Brauer algebra. This paper studies a q-deformation, B n r,s (q), of the walled Brauer algebra and shows that the centralizer algebra for the action of the quantum group UR(gl n) on mixed tensor...
متن کامل