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.
Noncommutative determinants, Cauchy-Binet formulae and Capelli-type identities. I. Generalizations of the Capelli and Turnbull identities / S. Caracciolo, A. D. Sokal, A. Sportiello. - In: ELECTRONIC JOURNAL OF COMBINATORICS. - ISSN 1077-8926. - 16:1(2009), pp. R103.1-R103.43.
Noncommutative determinants, Cauchy-Binet formulae and Capelli-type identities. I. Generalizations of the Capelli and Turnbull identities
S. CaraccioloPrimo
;A. SportielloUltimo
2009
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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
