Noncommutative determinants, Cauchy-Binet formulae and Capelli-type identities. I. Generalizations of the Capelli and Turnbull identities
Articolo
Data di Pubblicazione:
2009
Citazione:
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.
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Capelli identity; Cauchy-binet theorem; Cayley identity; Classical invariant theory; Columndeterminant; Determinant; Noncommutative determinant; Noncommutative ring; Permanent; Representation theory; Row-determinant; Turnbull identity; Weyl algebra
Elenco autori:
S. Caracciolo, A. D. Sokal, A. Sportiello
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