On a theorem of Lehrer and Zhang
Jun Hu
Zhankui Xiao
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Abstract
Let be an arbitrary field of characteristic not equal to 2. Let and be an dimensional orthogonal space over . There is a right action of the Brauer algebra 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 (see (1.1)) and proved that the annihilator of in 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 the symmetric groups of different sizes and a new integral basis for the annihilator of in .
Cite this article
Jun Hu, Zhankui Xiao, On a theorem of Lehrer and Zhang. Doc. Math. 17 (2012), pp. 245–270
DOI 10.4171/DM/367