A note on bideterminants for Schur superalgebras

作者:Marko Frantisek*; Zubkov Alexandr N
来源:Journal of Pure and Applied Algebra, 2011, 215(9): 2223-2230.
DOI:10.1016/j.jpaa.2011.02.003

摘要

Let S(m|n, r)(Z) be a Z-form of a Schur superalgebra S(m|n, r) generated by elements xi(i,j). We solve a problem of Muir and describe a Z-form of a simple S(m|n, r)-module D-lambda,D-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 [T-l : T-i] defined in this work. We also prove that each [T-l : T-i] is a Z-linear combination of modified bideterminants corresponding to (m|n)-semistandard tableaux T-i.

  • 出版日期2011-9

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