ALGEBRAIC COMBINATORICS

no. 3
The Hopf structure of symmetric group characters as symmetric functions
Orellana, Rosa1; Zabrocki, Mike2
1 Dartmouth College Mathematics Department Hanover, NH 03755, USA
2 Department of Mathematics and Statistics York University Toronto, Ontario M3J 1P3, Canada
Algebraic Combinatorics, Volume 4 (2021) no. 3, pp. 551-574.

In [24] 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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.170
Classification: 05E05, 05E10
Keywords: symmetric functions, symmetric group characters, Hopf algebra
Orellana, Rosa 1; Zabrocki, Mike 2

1 Dartmouth College Mathematics Department Hanover, NH 03755, USA
2 Department of Mathematics and Statistics York University Toronto, Ontario M3J 1P3, Canada
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Orellana, Rosa; Zabrocki, Mike. The Hopf structure of symmetric group characters as symmetric functions. Algebraic Combinatorics, Volume 4 (2021) no. 3, pp. 551-574. doi : 10.5802/alco.170. https://alco.centre-mersenne.org/articles/10.5802/alco.170/

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