On a theorem of Lehrer and Zhang
Documenta mathematica, Tome 17 (2012), pp. 245-270
Let K be an arbitrary field of characteristic not equal to 2. Let m,n∈N and V be an m dimensional orthogonal space over K. There is a right action of the Brauer algebra Bn(m) on the n-tensor space V⊗n which centralizes the left action of the orthogonal group O(V). Recently G.I. Lehrer and R.B. Zhang defined certain quasi-idempotents Ei in Bn(m) (see (1.1)) and proved that the annihilator of V⊗n in Bn(m) is always equal to the two-sided ideal generated by E[(m+1)/2] if charK=0 or charK>2(m+1). In this paper we extend this theorem to arbitrary field K with charK=2 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 V⊗m+1 in Bm+1(m).
Classification :
15A72, 16G99, 20B30
Mots-clés : Brauer algebras, tensor spaces, symmetric groups, standard tableaux
Mots-clés : Brauer algebras, tensor spaces, symmetric groups, standard tableaux
@article{10_4171_dm_367,
author = {Zhankui Xiao and Jun Hu},
title = {On a theorem of {Lehrer} and {Zhang}},
journal = {Documenta mathematica},
pages = {245--270},
year = {2012},
volume = {17},
doi = {10.4171/dm/367},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/367/}
}
Zhankui Xiao; Jun Hu. On a theorem of Lehrer and Zhang. Documenta mathematica, Tome 17 (2012), pp. 245-270. doi: 10.4171/dm/367
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