Abstract:   By using cutting strips and transformations on outside decompositions of a skew diagram, we show that the Giambelli type matrices of a skew Schur function are stably equivalent to each other over symmetric functions. As a consequence, the Jacobi-Trudi matrix and the dual Jacobi-Trudi matrix are stably equivalent over symmetric functions. This gives an armative answer to an open problem posed by Kuperberg.

  AMS Classification:  05E05, 05A15.

  Suggested Running Title:   The Giambelli type matrices. 

  Keywords:   Giambelli type matrix, Jacobi-Trudi matrix, dual Jacobi-Trudi matrix, stably equivalent, outside decomposition, cutting strip, twist transformation.

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