scholarly journals Multiparametric quantum deformation of the general linear supergroup

1989 ◽  
Vol 123 (1) ◽  
pp. 163-175 ◽  
Author(s):  
Yu. I. Manin
Keyword(s):  
General Linear ◽  
Quantum Deformation ◽  
General Linear Supergroup

COSTANDARD MODULES OVER SCHUR SUPERALGEBRAS IN CHARACTERISTIC p

2008 ◽  
Vol 07 (02) ◽  
pp. 147-166 ◽  
Author(s):  
ROBERTO LA SCALA ◽  
ALEXANDER ZUBKOV
Keyword(s):  
Null Space ◽  
General Linear ◽  
Base Field ◽  
Characteristic P ◽  
Schur Algebra ◽  
Arbitrary Characteristic ◽  
Linear Basis ◽  
General Linear Supergroup ◽  
Schur Superalgebra

In this paper we consider the problem of describing the costandard modules ∇(λ) of a Schur superalgebra S(m|n,r) over a base field K of arbitrary characteristic. Precisely, if G = GL(m|n) is a general linear supergroup and Dist (G) its distribution superalgebra we compute the images of the Kostant ℤ-form under the epimorphism Dist (G) → S(m|n,r). Then, we describe ∇(λ) as the null-space of some set of superderivations and we obtain an isomorphism ∇(λ) ≈ ∇(λ+|0) ⊗ ∇(0|λ-) assuming that λ = (λ+|λ-) and λm = 0. If char (K) = p we give a Frobenius isomorphism ∇(0|pμ) ≈ ∇(μ)p where ∇(μ) is a costandard module of the ordinary Schur algebra S(n,r). Finally we provide a characteristic free linear basis for ∇(λ|0) which is parametrized by a set of superstandard tableaux.

scholarly journals BLOCKS FOR THE GENERAL LINEAR SUPERGROUP GL(m|n)

2017 ◽  
Vol 23 (1) ◽  
pp. 185-215 ◽  
Author(s):  
F. MARKO ◽  
A. N. ZUBKOV
Keyword(s):  
General Linear ◽  
General Linear Supergroup
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