caa a22 4500 467911363 CHVBK 20180406152850.0 cr unu---uuuuu 170328e20060401xx s 000 0 eng 10.1007/s11232-006-0054-0 doi (NATIONALLICENCE)springer-10.1007/s11232-006-0054-0 Quantum matrix algebras of the GL ( mn ) type: The structure and spectral parameterization of the characteristic subalgebra [Elektronische Daten] [D. Gurevich, P. Pyatov, P. Saponov] We continue the study of quantum matrix algebras of the GL(m|n) type. We find three alternative forms of the Cayley-Hamilton identity; most importantly, this identity can be represented in a factored form. The factorization allows naturally dividing the spectrum of a quantum supermatrix into subsets of "even” and "odd” eigenvalues. This division leads to a parameterization of the characteristic subalgebra (the subalgebra of spectral invariants) in terms of supersymmetric polynomials in the eigenvalues of the quantum matrix. Our construction is based on two auxiliary results, which are independently interesting. First, we derive the multiplication rule for Schur functions s λ (M) that form a linear basis of the characteristic subalgebra of a Hecke-type quantum matrix algebra; the structure constants in this basis coincide with the Littlewood-Richardson coefficients. Second, we prove a number of bilinear relations in the graded ring Λ of symmetric functions of countably many variables. Springer Science+Business Media, Inc., 2006 quantum groups nationallicence supermatrices nationallicence Cayley-Hamilton theorem nationallicence Littlewood-Richardson rule nationallicence Gurevich D. Université de Valenciennes et du Hainaut-Cambrésis, Valenciennes, France aut Pyatov P. Max-Planck-Institut für Mathematik, Bonn, Germany aut Saponov P. Institute for High Energy Physics, Protvino, Moscow Oblast, Russia aut Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/1(2006-04-01), 460-485 0040-5779 147:1<460 2006 147 11232 https://doi.org/10.1007/s11232-006-0054-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0054-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gurevich D. Université de Valenciennes et du Hainaut-Cambrésis, Valenciennes, France aut NATIONALLICENCE 700 1- Pyatov P. Max-Planck-Institut für Mathematik, Bonn, Germany aut NATIONALLICENCE 700 1- Saponov P. Institute for High Energy Physics, Protvino, Moscow Oblast, Russia aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/1(2006-04-01), 460-485 0040-5779 147:1<460 2006 147 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer