Geodesic
A new plethysm formula for symmetric functions
Journal of Algebraic Combinatorics, Tome 8 (1998) no. 3, pp. 253-272.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This paper gives a new formula for the plethysm of power-sum symmetric functions and Schur symmetric functions with one part. The form of the main result is that for $p _{ m}$ ( x) ^$\circ s _{ a}$ ( x) = å $_{ T}$ w $^{ maj $_ m$ ( T)} s _{ sh( T)}$ ( x) $p_\mu (\underline x) \circ s$_a $(\underline x) = \sum\limits_T {\underline $omega^maj_mu(T) s_sh(T) $(\underline x)}$ where the sum is over semistandard tableaux $T$ of weight $a ^{ b }$, w $\underline \omega $is a root of unity, and maj å $_{ T}$ w $^{ maj $_ m$ ( T)}$ sum$\limits_T {\omega $^maj_mu(T) where the sum is over semistandard tableaux T of shape w $^{ maj $_ m$ ( T)} : T \omega $^maj_mu(T) :T . This generalizes J. Stembridge's result [11] on the eigenvalues of elements of the symmetric group acting on the Specht modules.
Keywords: symmetric function, plethysm, eigenvalue, representation of the symmetric group 
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     author = {Doran, William F.IV},
     title = {A new plethysm formula for symmetric functions},
     journal = {Journal of Algebraic Combinatorics},
     pages = {253--272},
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     volume = {8},
     number = {3},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1998__8_3_a1/}
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Doran, William F.IV. A new plethysm formula for symmetric functions. Journal of Algebraic Combinatorics, Tome 8 (1998) no. 3, pp. 253-272. http://geodesic.mathdoc.fr/item/JAC_1998__8_3_a1/