2001/06/11 by Amitai Regev, Regev, Amitai
Mathematics · #05E10 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E10
paper · pdf · doi:10.48550/arxiv.math/0106072
17 pages
openalex publication_date 2001/06/11 · arxiv created 2001/06/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Sn on V⊗ n by permuting coordinates. In the `super' (\Bbb Z2 graded) case V=V0⊕ V1, a ± sign is added [BR]. These actions give rise to the corresponding Schur algebras S(Sn,V). Here S(Sn,V) is compared with S(An,V), the Schur algebra corresponding to the alternating subgroup An⊂ Sn . 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 V0=dim V1, S(An,V) is isomorphic to the crossed-product algebra S(An,V)≅ S(Sn,V)×\Bbb Z2 .