We report about some results, interesting examples, problems and conjectures revolving around the parabolic Kostant partition functions, the parabolic Kostka polynomials and “saturation” properties of several generalizations of the Littlewood–Richardson numbers. The Contents contains the titles of main topics we are going to discuss in the present paper.
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Anatol N. Kirillov, An Invitation to the Generalized Saturation Conjecture. Publ. Res. Inst. Math. Sci. 40 (2004), no. 4, pp. 1147–1239DOI 10.2977/PRIMS/1145475445