Combinatorics of quiver polynomials

Ezra Miller

MSRI

March 5,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

Buch and Fulton defined quiver polynomials in a geometric context, and proved that these polynomials can be expressed as integer sums of products of Schur functions in differences of alphabets. Motivated by the fact that Littlewood-Richardson numbers are (very) special cases of the integer `quiver coefficients' appearing in these sums, Buch and Fulton conjectured that all quiver coefficients are positive, and moreover described certain `factor sequenes' of Young tableaux that they should count.

The first thing I'll do in this talk is present an elementary definition of quiver polynomials, with no reference to geometry, in terms of combinatorial permutation diagrams called `pipe dreams' (`rc-graphs'). Then I'll talk about the algebraic combinatorics that goes into extracting sequences of Young tableaux from them. It would help to know what Schur functions and Young tableaux are, but everything else I'll define from scratch. This talk concerns joint work with Allen Knutson and Mark Shimozono.


Speaker's Contact Info: emiller(at-sign)msri.org


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