Related papers: On a theorem of Lehrer and Zhang

Let $m, n\in{\mathbb N}$. In this paper we study the right permutation action of the symmetric group ${\mathfrak S}_{2n}$ on the set of all the Brauer $n$-diagrams. A new basis for the free ${\mathbb Z}$-module ${\mathfrak B}_n$ spanned by…

We prove Schur--Weyl duality between the Brauer algebra $\mathfrak{B}_n(m)$ and the orthogonal group $O_{m}(K)$ over an arbitrary infinite field $K$ of odd characteristic. If $m$ is even, we show that each connected component of the…

In this paper we prove Schur-Weyl duality between the symplectic group and Brauer algebra over an arbitrary infinite field $K$. We show that the natural homomorphism from the Brauer algebra $B_n(-2m)$ to the endomorphism algebra of tensor…

Let $m,n\in \mathbb{N}$, and $V$ be a $m$-dimensional vector space over a field $F$ of characteristic $0$. Let $U=F\oplus V$ and $R_n$ be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of…

Let $V=\C^n$ be endowed with an orthogonal form and $G=\Or(V)$ be the corresponding orthogonal group. Brauer showed in 1937 that there is a surjective homomorphism $\nu:B_r(n)\to\End_G(V^{\otimes r})$, where $B_r(n)$ is the $r$-string…

Let ${\mathcal P}{\mathcal M}^\alpha_s$ be a moduli space of stable parabolic vector bundles of rank $n \geq 2$ and fixed determinant of degree $d$ over a compact connected Riemann surface $X$ of genus $g(X) \geq 2$. If $g(X) = 2$, then we…

We study the representation theory of the braids and ties algebra, or the $bt$-algebra, $ \cal E$. Using the cellular basis $\{m_{{\mathfrak s} {\mathfrak t}} \}$ for $ \cal E$ obtained in previous joint work with J. Espinoza we introduce…

A category of Brauer diagrams, analogous to Turaev's tangle category, is introduced, and a presentation of the category is given; specifically, we prove that seven relations among its four generating homomorphisms suffice to deduce all…

If $E$ is a graph and $K$ is a field, we consider an ideal $I$ of the Leavitt path algebra $L_K(E)$ of $E$ over $K$. We describe the admissible pair corresponding to the smallest graded ideal which contains $I$ where the grading in question…

This paper addresses a conjecture of Kadison and Kastler that a von Neumann algebra M on a Hilbert space H should be unitarily equivalent to each sufficiently close von Neumann algebra N and, moreover, the implementing unitary can be chosen…

We prove that any Bernstein algebra $(A, \omega)$ is isomorphic to a semidirect product $V \ltimes_{(\cdot, \, \Omega)} \, k$ associated to a commutative algebra $(V, \cdot)$ such that $(x^2)^2 = 0$, for all $x\in A$ and an idempotent…

We define an extension of the affine Brauer algebra, the type B/C affine Brauer algebra. This new algebra contains the hyperoctahedral group and it naturally acts on $END_K(X \otimes V^{\otimes k})$ for Orthogonal and Symplectic groups.…

The first fundamental theorem of invariant theory for the orthosymplectic supergroup ${\rm OSp}(V)$ (where $V$ has superdimension $(m|2n)$) in the endomorphism algebra setting states that there is a surjective algebra homomorphism $F_r^r:…

Let $K$ be a field of characteristic zero and $V$ a vector space of dimension $m>1$ with a nondegenerate symmetric bilinear form $f:V\times V \rightarrow K$. The Jordan algebra $B_m=K\oplus V$ of the form $f$ is a superalgebra with this…

The classical characteristic map associates symmetric functions to characters of the symmetric groups. There are two natural analogues of this map involving the Brauer algebra. The first of them relies on the action of the orthogonal or…

For every partition $\lambda$ of a positive integer $n$, let $S^{\lambda}$ be the corresponding Specht module of the symmetric group $\mathfrak{S}_n$, and let $\det(\lambda)\in \mathbb Z$ denote the Gram determinant of the canonical…

We derive a general result about commuting actions on certain objects in braided rigid monoidal categories. This enables us to define an action of the Brauer algebra on the tensor space $V^{\otimes k}$ which commutes with the action of the…

We bound the symbol length of elements in the Brauer group of a field $K$ containing a $C_m$ field (for example any field containing an algebraically closed field or a finite field), and solve the local exponent-index problem for a $C_m$…

Let $V^{\otimes n}$ be the $n$-fold tensor product of a vector space $V.$ Following I. Schur we consider the action of the symmetric group $S_n$ on $V^{\otimes n}$ by permuting coordinates. In the `super' ($\Bbb Z_2$ graded) case…

In [ZH], R.B. Zhang found a way to link certain formal deformations of the Lie algebra o(2l+1) and the Lie superalgebra osp(1,2l). The aim of this article is to reformulate the Zhang transformation in the context of the quantum enveloping…