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This article is cited in 2 scientific papers (total in 2 papers)
Research Papers
Inverting the Frobenius map
S. Fominab, J.-Y. Thibonc a St. Petersburg Institute of Informatics Russian Academy of Sciences
b Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA
c Institut Gaspard-Monge Institute, Université de Marne-la-Vallée, France
Abstract:
The famous Frobenius characteristic map is a bijection from the space of
characters of the symmetric group $S_n$ to the space of homogeneous symmetric functions
of degree $n$. In this note, a formula for the inverse map is proved. More precisely, the
generating function for the values of an arbitrary virtual character $\chi$ of $S_n$ is expressed
in terms of the symmetric function which is the Frobenius image of $\chi$.
We also give a $q$-analogue of this result by providing a similar formula for the Hecke
algebra characters, and suggest some applications.
Received: 21.02.1997
Citation:
S. Fomin, J.-Y. Thibon, “Inverting the Frobenius map”, Algebra i Analiz, 10:3 (1998), 183–192; St. Petersburg Math. J., 10:3 (1999), 545–552
Linking options:
https://www.mathnet.ru/eng/aa1014 https://www.mathnet.ru/eng/aa/v10/i3/p183
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