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Double Centralizing Theorems for the Alternating Groups

✍ Scribed by Amitai Regev

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 148 KB
Volume: 250
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.9091

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✦ Synopsis

Let V ⊗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 ⊗n by permuting coordinates. In the super ( 2 graded) case V = V 0 ⊕ V 1 , a ± sign is added. These actions give rise to the corresponding Schur algebras S S n V . Here S S n V is compared with S A n V , the Schur algebra corresponding to the alternating subgroup A n ⊂ S n . While in the classical (signless) case these two Schur algebras are the same for n large enough, it is proved that in the super case, where dim V 0 = dim V 1 , S A n V is isomorphic to the cross-product algebra S A n V ∼ = S S n V ⊗ 2 .  2002 Elsevier Science (USA)

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