Proves Fredholm determinantal identity for tilted Toeplitz minors generalizing BOGC, with bialternant forms, Cauchy-Binet expansions, and asymptotic links to Airy kernel perturbations.
Cofactors and eigenvectors of banded Toeplitz matrices: Trench formulas via skew Schur polynomials
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abstract
The Jacobi-Trudi formulas imply that the minors of the banded Toeplitz matrices can be written as certain skew Schur polynomials. In 2012, Alexandersson expressed the corresponding skew partitions in terms of the indices of the struck-out rows and columns. In the present paper, we develop the same idea and obtain some new applications. First, we prove a slight generalization and modification of Alexandersson's formula. Then, we deduce corollaries about the cofactors and eigenvectors of banded Toeplitz matrices, and give new simple proofs to the corresponding formulas published by Trench in 1985.
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math.FA 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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A Borodin-Okounkov-Geronimo-Case identity for tilted Toeplitz minors
Proves Fredholm determinantal identity for tilted Toeplitz minors generalizing BOGC, with bialternant forms, Cauchy-Binet expansions, and asymptotic links to Airy kernel perturbations.