111 research outputs found
An Invitation to the Generalized Saturation Conjecture
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.Comment: 79 pages, new sections, new results and example
Skew Divided Difference Operators and Schubert Polynomials
We study an action of the skew divided difference operators on the Schubert
polynomials and give an explicit formula for structural constants for the
Schubert polynomials in terms of certain weighted paths in the Bruhat order on
the symmetric group. We also prove that, under certain assumptions, the skew
divided difference operators transform the Schubert polynomials into
polynomials with positive integer coefficients.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on
Integrable Systems and Related Topics, published in SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
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