Mathematics Colloquia and Seminars
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Combinatorics of quiver polynomialsAlgebra & Discrete Mathematics
|Speaker: ||Ezra Miller, Univ of Minnesota and MSRI Berkeley|
|Location: ||593 Kerr|
|Start time: ||Thu, Apr 24 2003, 12:00PM|
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.
After indicating in an elementary way how quiver polynomials are
defined via geometry, I will discuss combinatorial formulae for
them that arise on the way to a solution of the Buch-Fulton
conjecture. I will define everything from scratch, although
previous familiarity with Schur functions will help in
understanding the combinatorial motivations. This talk oncerns
joint work with Allen Knutson and Mark Shimozono.