Ubiquity of Kostka polynomials

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dc.creatorKirillov, Anatol N.
dc.date1999-12-12
dc.date2000-11-27
dc.date.accessioned2026-07-07T05:32:14Z
dc.date.available2026-07-07T05:32:14Z
dc.descriptionWe report about results revolving around Kostka-Foulkes and parabolic Kostka polynomials and their connections with Representation Theory and Combinatorics. It appears that the set of all parabolic Kostka polynomials forms a semigroup, which we call {\it Liskova semigroup}. We show that polynomials frequently appearing in Representation Theory and Combinatorics belong to the Liskova semigroup. Among such polynomials we study rectangular $q$-Catalan numbers; generalized exponents polynomials; principal specializations of the internal product of Schur functions; generalized $q$-Gaussian polynomials; parabolic Kostant partition function and its $q$-analog; certain generating functions on the set of transportation matrices. In each case we apply rigged configurations technique to obtain some interesting and new information about Kostka-Foulkes and parabolic Kostka polynomials, Kostant partition function, MacMahon, Gelfand-Tsetlin and Chan-Robbins polytopes. We describe certain connections between generalized saturation and Fulton's conjectures and parabolic Kostka polynomials; domino tableaux and rigged configurations. We study also some properties of $l$-restricted generalized exponents and the stable behaviour of certain Kostka-Foulkes polynomials.
dc.descriptionLaTeX, 104 pages, revised version, many new exercises added (about 35 pages), and some typos are corrected
dc.identifierhttps://arxiv.org/abs/math/9912094
dc.identifierhttp://arxiv.org/abs/math/9912094
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79590
dc.subjectQuantum Algebra
dc.subjectCombinatorics
dc.titleUbiquity of Kostka polynomials
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