Remarks concerning linear characters of reflection groups

Remarks concerning Linear Characters of Reflection Groups

Let G be a finite group generated by unitary reflections in a Hermitian space V , and let ζ be a root of unity. Let E be a subspace of V , maximal with respect to the property of being a ζ-eigenspace of an element of G, and let C be the parabolic subgroup of elements fixing E pointwise. If χ is any linear character of G, we give a condition for the restriction of χ to C to be trivial in terms o...

Some Examples and Remarks Concerning Groups

We present some examples and remarks which may be helpful to those who are dealing with an abstract algebra or a first semester group theory course. Alternating groups, dihedral groups, and symmetric groups of small orders are treasure troves of elementary examples and counter examples concerning groups. Mathematics Subject Classification: 20-01, 20-02, 20B05, 20B07, 20E06

On the Restriction of Characters of Special Linear Groups of Dimension Three

Brauer Groups of Linear Algebraic Groups with Characters

Let G be a connected linear algebraic group over an algebraically closed field of characteristic zero. Then the Brauer group of G is shown to be C X (Q/Z)<n) where C is finite and n = d(d l)/2, with d the Z-Ta.nk of the character group of G. In particular, a linear torus of dimension d has Brauer group (Q/Z)(n) with n as above. In [6], B. Iversen calculated the Brauer group of a connected, char...

On Characters of Irreducible Unitary Representations of General Linear Groups

Founding harmonic analysis on classical simple complex groups, I.M. Gelfand and M.A. Naimark in their classical book [GN] posed three basic questions: unitary duals, characters of irreducible unitary representations and Plancherel measures. In the case of reductive p-adic groups, the only series of reductive groups where unitary duals are known are general linear groups. In this paper we reduce...