Details

Autor(en) / Beteiligte

• Marko, František

Titel

Symmetrizers for Schur superalgebras

Ist Teil von

• Journal of pure and applied algebra, 2023-02, Vol.227 (2), p.107189, Article 107189

Ort / Verlag

Elsevier B.V

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• For the Schur superalgebra S=S(m|n,r) over a ground field K of characteristic zero, we define the symmetrizer Tλ[i:j] of the ordered pairs of tableaux (Ti,Tj) of the shape λ. We show that the K-span Aλ,K of all symmetrizers Tλ[i:j] has a basis consisting of Tλ[i:j] for Ti and Tj semistandard. In particular, Aλ,K≠0 if and only if λ is an (m|n)-hook partition. In this case, the S-superbimodule Aλ,K is identified as Dλ⊗KDλo, where Dλ and Dλo are left and right irreducible S-supermodules of the highest weight λ. We define modified symmetrizers Tλ{i:j} and show that their Z-span forms a Z-form Aλ,Z of Aλ,Q. We show that every modified symmetrizer Tλ{i:j} is a Z-linear combination of modified symmetrizers Tλ{i:j} for Ti,Tj semistandard. Using modular reduction to a field K of characteristic p>2, we obtain that Aλ,K has a basis consisting of modified symmetrizers Tλ{i:j} for Ti and Tj semistandard.