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Rosa Orellana, Dartmouth College, “The partition algebra, symmetric functions and Kronecker coefficients”

March 20, 2017 | 3:00 pm - 4:00 pm EDT

The Schur-Weyl duality between the symmetric group and the general linear group allows us to connect the representation theory of these two groups. A consequence of this duality is the Frobenius formula which connects the irreducible characters of the general linear group and the symmetric group via symmetric functions.

The symmetric group is also in Schur Weyl duality with the partition algebra. This duality allows us to introduce a new Frobenius type formula that connects the characters of the symmetric group and those of the partition algebra. In this talk we introduce a new basis of the ring of symmetric functions which specialize to the characters of the symmetric group when evaluated at roots of unity. Furthermore, the structure coefficients for this new basis of symmetric functions are the stable (or reduced) Kronecker coefficients. We will also discuss how this new basis allows us to use symmetric functions to study the representation theory of the partition algebra and the Kronecker coefficients.

This is joint work with Mike Zabrocki.

 

Details

Date:
March 20, 2017
Time:
3:00 pm - 4:00 pm EDT
Event Category:

Venue

SAS 4201