We use the theory of U q-tilting modules to construct cellular bases for centralizer algebras.
Our methods are quite general and work for any quantum group U q attached to a Cartan …

arXiv:math/0601387v2 [math.RT] 18 Jan 2007 Page 1 arXiv:math/0601387v2 [math.RT] 18
Jan 2007 THE BLOCKS OF THE BRAUER ALGEBRA IN CHARACTERISTIC ZERO ANTON …

Let V be a free module of rank n over a commutative ring. We prove that tensor space V⊗ r
satisfies Schur–Weyl duality, regarded as a bimodule for the action of the group algebra of …

Let l, n∈ N. Let sp2l be the symplectic Lie algebra over the complex number field C. Let V
be the natural representation of the quantized enveloping algebra Uq (sp2l) and Bn, q the …

We study invariant theory of the general linear supergroup in positive characteristic. In
particular, we determine when the symmetric group algebra acts faithfully on tensor …

It is a well-established fact in quantum information theory, that uniform averaging over the
collective action of a unitary group on a multipartite quantum state projects the state to a form …

We prove an integral version of the Schur–Weyl duality between the specialized Birman–
Murakami–Wenzl algebra $\mathfrak {B} _n (-q^{2m+ 1}, q) $ and the quantum algebra …

Let k be an algebraically closed field of characteristic p> 0, let m, r be integers with m≥ 1,
r≥ 0 and m≥ r and let S 0 (2 m, r) be the symplectic Schur algebra over k as introduced by …

The rook monoid, also known as the symmetric inverse monoid, is the archetypal structure
when it comes to extend the principle of symmetry. In this paper, we establish a Schur–Weyl …

Let OSp (V) be the orthosymplectic supergroup on an orthosymplectic vector superspace V
of superdimension (m| 2 n). Lehrer and Zhang showed that there is a surjective algebra …