20 03 Berezinians , Exterior Powers and Recurrent Sequences

A ug 2 00 4 BEREZINIANS , EXTERIOR POWERS AND RECURRENT SEQUENCES

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, w...

Powers in Sturmian sequences

New Plethysm Operation, Chern Characters of Exterior and Symmetric Powers with Applications to Stiefel-Whitney Classes of Grassmannians

Svctan, D., New plethysm operation, Checn characters of exterior and symmetric powers with applications to Stiefel-Whitney classes of gcassmannians, Theoretical Computer Science 117 (1993) 289-301. In this paper a new plethysm operation is proposed and a technique for coefficient extraction for a fairly general class of symmetric power series (e.g. multiplicative sequences of the theory of ?cha...

Exterior Powers of Symmetric Bilinear Forms

We study exterior powers of classes of symmetric bilinear forms in the WittGrothendieck ring of a field of characteristic not equal to 2, and derive their basic properties. The exterior powers are used to obtain annihilating polynomials for quadratic forms in the Witt ring. 1991 AMS Subject Classification: 11E04, 11E81

Exterior Powers

Let R be a commutative ring. Unless indicated otherwise, all modules are R-modules and all tensor products are taken over R, so we abbreviate ⊗R to ⊗. A bilinear function out of M1 × M2 turns into a linear function out of the tensor product M1 ⊗ M2. In a similar way, a multilinear function out of M1 × · · · ×Mk turns into a linear function out of the k-fold tensor product M1 ⊗ · · · ⊗Mk. We wil...