On irreducibility of induced modules and an adaptation of the Wigner--Mackey method of little groups
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This paper deals with sufficiency conditions for irreducibilityof certain induced modules. We also construct irreducible representationsfor a group G over a field K where the group G is a semidirect product ofa normal abelian subgroup N and a subgroup H. The main results areproved with the assumption that char K does not divide |G| but there isno assumption made of K being algebraically closed.
Abstract
This paper deals with sufficiency conditions for irreducibilityof certain induced modules. We also construct irreducible representationsfor a group G over a field K where the group G is a semidirect product ofa normal abelian subgroup N and a subgroup H. The main results areproved with the assumption that char K does not divide |G| but there isno assumption made of K being algebraically closed.
참고문헌 (5)
- Charles W, "Curtis and Irving Reiner, Representation Theory of Finite Groups and As- sociative Algebras" (1962), Interscience Publishers
- Charles W, "Methods of Representation Theory. Vol. I" (1981), Wiley Interscience
- G. Karpilovsky, "Induced Modules over Group Algebras" (1990), North-Holland
- G.W. Mackey, "On induced representations of grou", Amer. J. Math, 73, pp.576~592 (1951)
- J.-P. Serre, "Linear Representations of Finite Groups" (1977), Springer-Verlag