Which finite groups have no irreducible representations other than ...

A classical result states that all the irreducible representations of a finite group over C are characters if and only if G is abelian.

Infinite groups in which all irreducible representations are one ...

If you restrict attention to finite-dimensional representations, then such groups exist; that is, there are infinite nonabelian groups all ...

Irreducible representation - Wikipedia

Irreducible representations are always indecomposable (ie cannot be decomposed further into a direct sum of representations), but the converse may not hold.

Representation theory of finite groups - Wikipedia

To achieve a unique decomposition, one has to combine all the irreducible subrepresentations that are isomorphic to each other. That means, the representation ...

REPRESENTATION THEORY FOR FINITE GROUPS

In later sections, we develop the tools to show that this two-dimensional represen- tation is, in fact, irreducible. Besides the notion of ...

Non-unitary, finite dimensional representations of the Lorentz group

On Wikipedia and often in physics books it is stated, that the Lorenz group's finite dimensional non-unitary representations are completely ...

Everything about Representation theory of finite groups : r/math

The group is a cyclic group generated by the element Ta, where Ta is a translation by one 'unit cell.' Cyclic in this case means any general T = ...

Groups having a faithful irreducible representation - ScienceDirect

We address the problem of finding necessary and sufficient conditions for an arbitrary group, not necessarily finite, to admit a faithful ...

Finite Groups and Character Theory 1 Representations of Finite ...

A group G is said have the property of complete reducibility if any representation can be decomposed into a direct sum of irreducible representations. Theorem 1 ...

COMPUTING IRREDUCIBLE REPRESENTATIONS OF FINITE ...

aspects of this latter have been considered for nonabelian groups by. Atkinson [1], Beth [4], Clausen [10, 11], Diaconis and Rockmore [15], and others.

Representation Theory

Any irreducible complex representation of a cyclic group is 1-dimensional. Proof. Cyclic groups are abelian. By the preceding corollary, we are ...

Representation Theory - UC Berkeley math

This will be proved for complex representations of finite groups. 2.14 Definition. A representation is called irreducible if it contains no proper invariant sub ...

Irreducible representations of $G_4 = \langle a,b \mid a^{16}, b^{2 ...

These are generally called semidihedral groups. The irreducible representations all have degree 1 or 2, four of degree ...

Irreducible Representations of Finite Groups of Lie Type

... any case, f(α) < 1, and therefore that the Steinberg representation has larger degree than any other unipotent representation for G a finite group of ...

Irreducible Representations of C*-crossed products by Finite Groups

of an irreducible representation of A Χ G to A does not lead to an irreducible representation of A, we need a different approach than [11]. The main tool we ...

Notes on Representations of Finite Groups

... that the dimension of any irreducible representation divides the order of the group. ... Since f is irreducible and has degree more than 1, f does not have a root ...

Groups whose irreducible representations have degree at most 2

Let F be an algebraically closed field of characteristic different from 2. We classify the finite groups G for which every irreducible F -representation of ...

Representation Theory of Finite Groups - arXiv

Let χ be a non-linear (i.e., dimension is greater than 1) irreducible ... if V1 and V2 do not have a common irreducible representation when they are written as a.

Irreducible representations of finite groups in the T-matrix ...

It is straightforward to apply the method to derive a more complete list of reducible representations. The results are presented below. This list covers all ...

Irreducible adjoint representations in prime power dimensions, with ...

In this case, the groups G are taken to be the normalizers of certain extraspecial groups (the analogue of the Heisenberg groups over finite fields). More ...