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[PAST EVENT] Mathematics Colloquium
March 23, 2012
2pm - 3pm
Title: Hessenberg representations and the chromatic symmetric function.
Abstract:
A polynomial in n-variables is called symmetric if it is unchanged after any permutation of the variables. A representation of the symmetric group is a vector space which carries a linear action of the symmetric group. These two theories have many fascinating connections with the combinatorics of partitions and tableaux. In fact, the Frobenius characteristic map allows questions in one theory to be rephrased in the language of the other. In this talk we describe a conjectural connection between a family of symmetric functions called the chromatic symmetric functions and a family of representations of the symmetric group arising from spaces called Hessenberg varieties. We will show how a positive answer to this conjecture can be obtained by counting a special family of tableaux.
Abstract:
A polynomial in n-variables is called symmetric if it is unchanged after any permutation of the variables. A representation of the symmetric group is a vector space which carries a linear action of the symmetric group. These two theories have many fascinating connections with the combinatorics of partitions and tableaux. In fact, the Frobenius characteristic map allows questions in one theory to be rephrased in the language of the other. In this talk we describe a conjectural connection between a family of symmetric functions called the chromatic symmetric functions and a family of representations of the symmetric group arising from spaces called Hessenberg varieties. We will show how a positive answer to this conjecture can be obtained by counting a special family of tableaux.
Contact
[[vinroot, Ryan Vinroot]]