منابع مشابه
On Degrees of Irreducible Brauer Characters
Based on a large amount of examples, which we have checked so far, we conjecture that |G|p′ ≤ ∑ φ φ(1) 2 where p is a prime and the sum runs through the set of irreducible Brauer characters in characteristic p of the finite group G. We prove the conjecture simultaneously for p-solvable groups and groups of Lie type in the defining characteristic. In non-defining characteristics we give asymptot...
متن کاملA Note on Lifting Brauer Characters
A Brauer character of a finite group may be lifted to an ordinary character if it lies in a block whose defect groups are contained in a normal p-solvable subgroup. By the Fong-Swan theorem [2, Theorem 72.1], an irreducible Brauer character of a finite p-solvable group G may be lifted to an ordinary (complex) character of G. In other words, every Brauer character is the restriction of some ...
متن کاملA ‘Second Orthogonality Relation’ for Characters of Brauer Algebras
In a first course in representation theory , one usually learns that there are two important relations for characters of a finite group , the first orthogonality relation and the second orthogonality relation . When one moves on to study algebras which are not necessarily group algebras it is not clear , a priori , that the study of characters would be fruitful , and one encounters various prob...
متن کاملBrauer 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...
متن کاملA 'Second Orthogonality Relation' for Characters of Brauer Algebras
0. Introduction In a rst course in representation theory one usually learns that there are two important relations for characters of a nite group, the rst orthogonality relation and the second orthogonality relation. When one moves on to study algebras which are not necessarily group algebras it is not clear, apriori, that the study of characters would be fruitful, and one encounters various pr...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2014
ISSN: 0001-8708
DOI: 10.1016/j.aim.2014.02.014