Stable Equivalences of Giambelli Type Matrices of Schur Functions

Details Stable Equivalences of Giambelli Type Matrices of Schur Functions Stable Equivalences of Giambelli Type Matrices of Schur Functions

2005-07-30

arxiv.org/abs/math/0508008v1

Mathematics

Combinatorics

16 pages, 4 figures

Scientific paper

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 affirmative answer to an open problem posed by Kuperberg.

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