Details:

Title
Author(s)	Shmuel Onn
Type	Technical Report, Misc
Abstract	Each matrix representation pi : G --> GL_n (K) of a finite group G over a field K induces an action of G on the module A^n over the polynomial algebra A = K[x_1, ... , x_n]. The graded A-submodule M(pi) of A^n generated by the orbit of (x_1, ... , x_n) is studied. A decomposition of M(pi) into generic modules is given. Relations between the numerical invariants of pi and those of M(pi), the later being efficiently computable by Groebner bases methods, are examined. It is shown that if pi is multiplicity-free, then the dimensions of the irreducible constituents of pi can be read off from the Hilbert series of M(pi). It is proved that determinantal relations form Groebner bases for the syzygies on generic matrices with respect to any lexicographic order. Groebner 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.
Length	20
File
Language	English
Year	1994
Edition	0
Translation	No
Refereed	No