The lattice permutation condition for Kronecker tableaux (Extended Abstract)

Bowman, C.; Visscher, Maud De; Enyang, John

doi:10.48550/arxiv.1812.09175

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2019

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“…In addition, we have shown in [OZ] that the structure coefficient of the {s λ } basis are the reduced (or stable) Kronecker coefficients, ḡγ α,β [Aiz,BDE,BO,BDO,BOR1,BOR,EA,Mur,Mur2,Mur3]. The history of these problems indicates that they are difficult and are unlikely to be resolved in a single step.…”

Section: Introductionmentioning

confidence: 99%

The Hopf structure of symmetric group characters as symmetric functions

Orellana¹,

Zabrocki²

2019

Preprint

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In [OZ] the authors introduced inhomogeneous bases of the ring of symmetric functions. The elements in these bases have the property that they evaluate to characters of symmetric groups. In this article we develop further properties of these bases by proving product and coproduct formulae. In addition, we give the transition coefficients between the elementary symmetric functions and the irreducible character basis.

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