Berezinians, exterior powers and recurrent sequences

Khudaverdian, Hovhannes M. and Voronov, Theodore (2005) Berezinians, exterior powers and recurrent sequences. Letters in Mathematical Physics, 74 (2). pp. 201-228. ISSN 1573-0530

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Abstract

Abstract We study power expansions of the characteristic function of a linear operator A in a p|q-dimensional superspace V. We show that traces of exterior powers of A satisfy universal recurrence relations of period q. ‘Underlying’ recurrence relations hold in the Grothendieck ring of representations of GL(V). They are expressed by vanishing of certain Hankel determinants of order q+1 in this ring, which generalizes the vanishing of sufficiently high exterior powers of an ordinary vector space. In particular, this allows to express the Berezinian of an operator as a ratio of two polynomial invariants. We analyze the Cayley–Hamilton identity in a superspace. Using the geometric meaning of the Berezinian we also give a simple formulation of the analog of Cramer’s rule

Item Type: Article
Uncontrolled Keywords: Berezinian - exterior powers of a superspace - invariants of supermatrices - recurrent sequences - Hankel determinants
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 58 Global analysis, analysis on manifolds
MSC 2010, the AMS's Mathematics Subject Classification > 81 Quantum theory
Depositing User: Ms Lucy van Russelt
Date Deposited: 14 Aug 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/490

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