26 research outputs found
On a theorem of Lehrer and Zhang
Let be an arbitrary field of characteristic not equal to 2. Let and an dimensional orthogonal space over . There is a right
action of the Brauer algebra \bb_n(m) on the -tensor space
which centralizes the left action of the orthogonal group . Recently G.I.
Lehrer and R.B. Zhang defined certain quasi-idempotents in \bb_n(m)
(see (\ref{keydfn})) and proved that the annihilator of in
\bb_n(m) is always equal to the two-sided ideal generated by
if or . In this paper we extend this theorem to
arbitrary field with 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 in \bb_{m+1}(m).Comment: big revision on Section