Noncommutative symmetric functions

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dc.creatorGelfand, Israel
dc.creatorKrob, D.
dc.creatorLascoux, Alain
dc.creatorLeclerc, B.
dc.creatorRetakh, V. S.
dc.creatorThibon, J. -Y.
dc.date1994-07-20
dc.date.accessioned2026-07-07T09:14:21Z
dc.date.available2026-07-07T09:14:21Z
dc.descriptionThis paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables. This allows us to endow the resulting algebra with a Hopf structure, which leads to a new method for computing in descent algebras. It also gives unified reinterpretation of a number of classical constructions. Next, we study the noncommutative analogs of symmetric polynomials. One arrives at different constructions, according to the particular kind of application under consideration. For example, when a polynomial with noncommutative coefficients in one central variable is decomposed as a product of linear factors, the roots of these factors differ from those of the expanded polynomial. Thus, according to whether one is interested in the construction of a polynomial with given roots or in the expansion of a product of linear factors, one has to consider two distinct specializations of the formal symmetric functions. A third type appears when one looks for a noncommutative generalization of applications related to the notion of characteristic polynomial of a matrix. This construction can be applied, for instance, to the noncommutative matrices formed by the generators of the universal enveloping algebra $U(gl_n)$ or of
dc.description111 pages
dc.identifierhttps://arxiv.org/abs/hep-th/9407124
dc.identifierhttp://arxiv.org/abs/hep-th/9407124
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152643
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleNoncommutative symmetric functions
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