TY - JOUR

T1 - A note on bideterminants for Schur superalgebras

AU - Marko, Frantisek

AU - Zubkov, Alexandr N.

N1 - Funding Information:
The second author was supported by RFFI 10.01.00383 a. The authors would like to thank a referee for careful reading of the manuscript and helpful suggestions.

PY - 2011/9

Y1 - 2011/9

N2 - Let S(m|n,r)Z be a Z-form of a Schur superalgebra S(m|n,r) generated by elements ξi,j. We solve a problem of Muir and describe a Z-form of a simple S(m|n,r)-module Dλ,Q over the field Q of rational numbers, under the action of S(m|n,r)Z. This Z-form is the Z-span of modified bideterminants [Tℓ:Ti] defined in this work. We also prove that each [Tℓ:Ti] is a Z-linear combination of modified bideterminants corresponding to (m|n)-semistandard tableaux Ti.

AB - Let S(m|n,r)Z be a Z-form of a Schur superalgebra S(m|n,r) generated by elements ξi,j. We solve a problem of Muir and describe a Z-form of a simple S(m|n,r)-module Dλ,Q over the field Q of rational numbers, under the action of S(m|n,r)Z. This Z-form is the Z-span of modified bideterminants [Tℓ:Ti] defined in this work. We also prove that each [Tℓ:Ti] is a Z-linear combination of modified bideterminants corresponding to (m|n)-semistandard tableaux Ti.

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U2 - 10.1016/j.jpaa.2011.02.003

DO - 10.1016/j.jpaa.2011.02.003

M3 - Article

AN - SCOPUS:79953715626

VL - 215

SP - 2223

EP - 2230

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 9

ER -