Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a theorem of Lehrer and Zhang   Let $K$ be an arbitrary field of characteristic not equal to 2. Let $m,
n\in\N$ and $V$ an $m$ dimensional orthogonal space over $K$. There is a right
action of the Brauer algebra $\bb_n(m)$ on the $n$-tensor space $V^{\otimes n}$
which centralizes the left action of the orthogonal group $O(V)$. Recently G.I.
Lehrer and R.B. Zhang defined certain quasi-idempotents $E_i$ in $\bb_n(m)$
(see (\ref{keydfn})) and proved that the annihilator of $V^{\otimes n}$ in
$\bb_n(m)$ is always equal to the two-sided ideal generated by $E_{[(m+1)/2]}$
if $\ch K=0$ or $\ch K>2(m+1)$. In this paper we extend this theorem to
arbitrary field $K$ with $\ch K\neq 2$ as conjectured by Lehrer and Zhang. As a
byproduct, we discover a combinatorial identity which relates to the dimensions
of Specht modules over symmetric groups of different sizes and a new integral
basis for the annihilator of $V^{\otimes m+1}$ in $\bb_{m+1}(m)$.

21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat