Geodesic
Hilbert series of group representations and Gröbner bases for generic modules
Journal of Algebraic Combinatorics, Tome 3 (1994) no. 2, pp. 187-206.

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Summary: Each matrix representation $A = k[ x _{1}$ , frac14 , $x _{ n} ] {\rm A} = \kappa $[x_1 , $\ldots $,x_n ] The graded $( x _{1}$ , frac14 , $x _{ n} )$ (x_1 , $\ldots $,x_n ) is studied. A decomposition of $M( Pgr)$ into generic modules is given. Relations between the numerical invariants of $Pgr$ and those of $M( Pgr)$, the latter being efficiently computable by Gröbner bases methods, are examined. It is shown that if $Pgr$ is multiplicity-free, then the dimensions of the irreducible constituents of $Pgr$ can be read off from the Hilbert series of $M$(Pi;). It is proved that determinantal relations form Gröbner bases for the syzygies on generic matrices with respect to any lexicographic order. Gröbner bases for generic modules are also constructed, and their Hilbert series are derived. Consequently, the Hilbert series of $M$(Pi;) is obtained for an arbitrary representation.
Keywords: Gröbner basis, linear representation, generic module, computational algebra, finite group, Hilbert series 
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     author = {Onn, Shmuel},
     title = {Hilbert series of group representations and {Gr\"obner} bases for generic modules},
     journal = {Journal of Algebraic Combinatorics},
     pages = {187--206},
     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1994__3_2_a1/}
}
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Onn, Shmuel. Hilbert series of group representations and Gröbner bases for generic modules. Journal of Algebraic Combinatorics, Tome 3 (1994) no. 2, pp. 187-206. http://geodesic.mathdoc.fr/item/JAC_1994__3_2_a1/