Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities. I. Generalizations of the Capelli and Turnbull identities

Details Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities. I. Generalizations of the Capelli and Turnbull identities Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities. I. Generalizations of the Capelli and Turnbull identities

2008-09-20

arxiv.org/abs/0809.3516v2

Electron. J. Combin. 16(1), #R103 (2009)

Mathematics

Combinatorics

LaTeX2e, 43 pages. Version 2 corrects an error in the statements of Propositions 1.4 and 1.5 (see new Remarks in Section 4) an

Scientific paper

We prove, by simple manipulation of commutators, two noncommutative
generalizations of the Cauchy-Binet formula for the determinant of a product.
As special cases we obtain elementary proofs of the Capelli identity from
classical invariant theory and of Turnbull's Capelli-type identities for
symmetric and antisymmetric matrices.

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