The GL(m|n) type quantum matrix algebras II: the structure of the characteristic subalgebra and its spectral parameterization

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dc.creatorGurevich, Dimitri
dc.creatorPyatov, Pavel
dc.creatorSaponov, Pavel
dc.date2005-08-25
dc.date2005-09-07
dc.date.accessioned2026-07-07T05:22:42Z
dc.date.available2026-07-07T05:22:42Z
dc.descriptionIn our previous paper math.QA/0412192 the Cayley-Hamilton identity for the GL(m|n) type quantum matrix algebra was obtained. Here we continue investigation of that identity. We derive it in three alternative forms and, most importantly, we obtain it in a factorized form. The factorization leads to a separation of the spectra of the quantum supermatrix into the "even" and "odd" parts. The latter, in turn, allows us to parameterize the characteristic subalgebra (which can also be called the subalgebra of spectral invariants) in terms of the supersymmetric polynomials in the eigenvalues of the quantum supermatrix. For our derivation we use two auxiliary results which may be of independent interest. First, we calculate the multiplication rule for the linear basis of the Schur functions $s_λ(M)$ for the characteristic subalgebra of the Hecke type quantum matrix algebra. The structure constants in this basis are the Littlewood-Richardson coefficients. Second, we derive a series of bilinear relations in the graded ring $Λ$ of Schur symmetric functions in countably many variables.
dc.description28 pages; two remarks (at p.6 and pp.15-16) added; several typos corrected
dc.identifierhttps://arxiv.org/abs/math/0508506
dc.identifierhttp://arxiv.org/abs/math/0508506
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76160
dc.subjectQuantum Algebra
dc.subject81R50; 16S37; 15A24
dc.titleThe GL(m|n) type quantum matrix algebras II: the structure of the characteristic subalgebra and its spectral parameterization
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