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arXiv · 0809.3516

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

Sergio Caracciolo·Andrea Sportiello·Alan D. Sokal
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Abstract

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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Sergio Caracciolo, Andrea Sportiello, Alan D. Sokal. 2009-08-11. Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities. I. Generalizations of the Capelli and Turnbull identities. https://doi.org/10.37236/192

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