Geodesic
A plethysm formula on the characteristic map of induced linear characters from \(U_n(\mathbb F_q)\) to \(GL(\mathbb F_q)\).
Zhi Chen1
1York University
The electronic journal of combinatorics, Tome 20 (2013) no. 3
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This paper gives a plethysm formula on the characteristic map of the induced linear characters from the unipotent upper-triangular matrices $U_n(\mathbb F_q)$ to $GL_n(\mathbb F_q)$, the general linear group over finite field $\mathbb F_q$. The result turns out to be a multiple of a twisted version of the Hall-Littlewood symmetric functions $\tilde{P}_n[Y;q]$. A recurrence relation is also given which makes it easy to carry out the computation.
DOI : 10.37236/2364
Classification : 20G05, 20C33, 20G40, 05E05
Mots-clés : general linear groups over finite fields, unipotent upper-triangular matrices, representations, induced characters, symmetric functions, supercharacters, Gelfand-Graev characters, plethysm, Hall-Littlewood functions

Zhi Chen  1

1 York University 
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     title = {A plethysm formula on the characteristic map of induced linear characters from {\(U_n(\mathbb} {F_q)\)} to {\(GL(\mathbb} {F_q)\).}},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {3},
     doi = {10.37236/2364},
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Zhi Chen. A plethysm formula on the characteristic map of induced linear characters from \(U_n(\mathbb F_q)\) to \(GL(\mathbb F_q)\).. The electronic journal of combinatorics, Tome 20 (2013) no. 3. doi: 10.37236/2364

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