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
SN - 0022-4049
VL - 215
SP - 2223
EP - 2230
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 9
ER -