Irreducible characters
Anchors of irreducible characters
... every irreducible character χ of a finite group G determines a unique conjugacy class of p-subgroups of G which we will call the anchors of ...to irreducible characters, such as defect groups, ...
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Factorizations in the Irreducible Characters of Compact Semisimple Lie Groups
... corresponding irreducible characters in E(G); such factors are necessarily W (G)-symmetric (since they are class functions on ...are irreducible characters which factor in E(G) even though the ...
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Irreducible characters of the unitriangular group and coadjoint orbits
... the irreducible characters o f the finite groups consisting of all the fixed elements of a Frobenius map defined on a unipotent algebraic group over an algebraically closed field of prime characteristic ...
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Finite simple groups with number of zeros slightly greater than the number of nonlinear irreducible characters
... Suppose that q ≡ 1 (mod 4), and write q = 4r + 1. Then G has a cyclic subgroup C of order 2r. If r ≥ 3, then C contains elements a, b, c of orders 2, r, 2r, respectively, so no two of them are conjugate in G. ...
8
On the number of the irreducible characters of factor groups
... Let G be a finite group and let N be a normal subgroup of G. Suppose that Irr(G|N ) is the set of the irreducible characters of G that contain N in their kernels. Our aim in this paper is to study the set ...
6
On the irreducible characters of the Weyl groups
... for Weyl groups of type B, similar to ones in types C and D §'.3 and §4.2, and include some results on inducing up irreducible characters from maximal Weyl subgroups of this group... WB [r] ...
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Finite groups with non-trivial intersections of kernels of all but one irreducible characters
... one irreducible characters or, equivalently, finite groups with an irreducible character vanishing on all but two conjugacy ...non-linear characters of distinct degrees, which were ...
18
Anchors of irreducible characters
... Permanent repository link: http://openaccess.city.ac.uk/13197/ Link to published version: http://dx.doi.org/10.1016/j.jalgebra.2015.11.034 Copyright and reuse: City Research Online aims [r] ...
6
Note on Heisenberg Characters of Heisenberg Groups
... The aim of this section is to compute the Heisenberg characters of five differ- ent types of Heisenberg groups. To do this, we first note that every linear character of a group G is Heisenberg. This proves that ...
9
Conjectures of Alperin and Broue for 2-blocks with elementary abelian defect groups of order 8
... all irreducible characters in the block have height zero (this is the ‘if’ part of Brauer’s height zero conjecture, which predicts that all characters in a block have height zero if and only if the ...
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On k(D) Blocks
... Our main concern is to study finite groups and their blocks which satisfy Definitions 1.1 and 1.2. Note that it is well known that k D ( ) is the number of the conjugacy classes of D . It is well known that blocks with ...
5
Irreducible Representations of Algebraic Group SL(6,K) in charK =3
... the irreducible cha- racters for other ...all irreducible characters for the simple algebraic groups of type A 5 over an algebraically closed field K of characteristic 3 with modified algorithm to ...
11
A characterisation of nilpotent blocks
... We refer to [17] for the notion and basic properties of hyperfocal subalgebras of source algebras of blocks. We show in this section that ordinary irreducible characters of the hyperfocal subalgebra of ...
12
On zero patterns of characters of finite groups
... It is well known that the set of values cd(G) = {χ(1) : χ ∈ Irr(G)} has a strong influence on the group structure of G, where Irr(G) denotes the set of irreducible complex characters of G. The aim of this ...
5
Simple Groups and Related Topics
... different irreducible characters; one of de- gree 2 and the other of degree 4, but the irreducible representation of degree 2 will give us an unfaithful linear ...linear irreducible character ...
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Dade’s ordinary conjecture implies the Alperin–McKay conjecture
... The proof combines arguments from Sambale [17] and formal properties of chains of subgroups in fusion systems from [7]. Let (K, O , k) be a p-modular system. We assume that k is algebraically closed, and let ¯ K be an ...
8
Character theory of infinite wreath products
... The representation theory of infinite wreath product groups is developed by means of the relationship between their group algebras and conjugacy classes with those of the infinite symmetric group. Further, since these ...
15
Primitive irreducible linear groups
... faithful irreducible module is simple, and by the well- known Wedderburn*s theorem (Huppert 1967* page 472), H j is thus isomorphic to a full kxk matrix ring over some ...
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THE THEORY OF REPRESENTATIONS OF GROUPS SO0(2; 1) AND ISO(2; 1). WIGNER COEFFICIENTS OF THE GROUP SO0(2; 1)
... Abstract. This paper is devoted to the representations of the groups SO(2, 1) and ISO(2, 1). Those groups have an important role in cosmology, elementary particle theory and mathematical physics. Irreducible ...
12
Class two p groups as fixed point free automorphism groups
... irreducible representations are cyclic or the central product of an extra special p group with a cycl i c group of.. That is, all irreducible r epresentations.[r] ...
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