Theory of monomial groups
نویسندگان
چکیده
منابع مشابه
Solvability of Generalized Monomial Groups
The solvability of monomial groups is a well-known result in character theory. Certain properties of Artin L-series suggest a generalization of these groups, namely to such groups where every irreducible character has some multiple which is induced from a character φ of U with solvable factor group U/ker(φ). Using the classification of finite simple groups, we prove that these groups are also s...
متن کاملMonomial Characters of Finite Groups
An abundance of information regarding the structure of a finite group can be obtained by studying its irreducible characters. Of particular interest are monomial characters — those induced from a linear character of some subgroup — since Brauer has shown that any irreducible character of a group can be written as an integral linear combination of monomial characters. Our primary focus is the cl...
متن کاملStandard Monomial Theory
We construct an explicit basis for the coordinate ring of the Bott-Samelson variety Zi associated to G = GL(n) and an arbitrary sequence of simple reflections i. Our basis is parametrized by certain standard tableaux and generalizes the Standard Monomial basis for Schubert varieties. In this paper, we prove the results announced in [LkMg] for the case of Type An−1 (the groups GL(n) and SL(n)). ...
متن کامل6 Generic Hecke Algebras for Monomial Groups
In this paper we define a two-variable, generic Hecke algebra, H, for each complex reflection group G(b, 1, n). The algebra H specializes to the group algebra of G(b, 1, n) and also to an endomorphism algebra of a representation of GLn(Fq) induced from a solvable subgroup. We construct Kazhdan-Lusztig “R-polynomials” for H and show that they may be used to define a partial order on G(b, 1, n). ...
متن کاملNew Algorithm For Computing Secondary Invariants of Invariant Rings of Monomial Groups
In this paper, a new algorithm for computing secondary invariants of invariant rings of monomial groups is presented. The main idea is to compute simultaneously a truncated SAGBI-G basis and the standard invariants of the ideal generated by the set of primary invariants. The advantage of the presented algorithm lies in the fact that it is well-suited to complexity analysis and very easy to i...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1942
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1942-0005739-6