Wednesday, May 6 2020
20:30 - 22:00

#### Livestream link: us02web.zoom.us/j/86726183427I will present a basis of the symmetric functions whose evaluations are irreduciblecharacters of the symmetric group in the same way that the evaluations of Schurfunctions are irreducible characters of the general linear group. These symmetricfunctions are related to character polynomials (that go back to a paper ofFrobenius in 1904) but they have the advantage that we are able to use the Hopfstructure of the symmetric functions to compute with them. In addition, theyindicate that the combinatorics of Kronecker coefficients is governed by multisettableaux. We use this basis to give a combinatorial interpretation for the tensorproducts of the form$$\chi^{(n-|\lambda|,\lambda)} \otimes \chi^{(n-a_1,a_1)} \otimes \chi^{(n-a_r,a_2)} \otimes \cdots \otimes \chi^{(n-a_r,a_r)}$$where $\lambda$ is a partition and $a_1, a_2, \ldots, a_r$ are non-negativeintegers.This is joint work with Rosa Orellana.

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