The character table of the fully nonrigid water cluster (cyclic forms), (H_{2}O){_i}, with C{_ih} symmetry derived for the first time, for 2<=i <=6. The group of all feasible permutations is the wreath product of groups S{_i}[S{_2}] which consists of i!2i operations for i = 2, ..., 6 divided into ( w.r.t) 5, 10, 20, 36, 65 conjugacy classes and 5, 10, 20, 36, 65 irreducible representations resp...

We study Shintani lifting of real-valued irreducible characters of finite reductive groups. In particular, if G is a connected reductive group defined over Fq, and ψ is an irreducible character of G(Fqm) which is the lift of an irreducible character χ of G(Fq), we prove ψ is real-valued if and only if χ is real-valued. In the case m = 2, we show that if χ is invariant under the twisting operato...

We have seen that irreducible representations of a compact Lie group G can be constructed starting from a highest weight space and applying negative roots to a highest weight vector. One crucial thing that this construction does not easily tell us is what the character of this irreducible representation will be. The character would tell us not just which weights occur in the representation, but...

we say that a finite group $g$ is conjugacy expansive if for anynormal subset $s$ and any conjugacy class $c$ of $g$ the normalset $sc$ consists of at least as many conjugacy classes of $g$ as$s$ does. halasi, mar'oti, sidki, bezerra have shown that a groupis conjugacy expansive if and only if it is a direct product ofconjugacy expansive simple or abelian groups.by considering a character analo...

Kriegel's self-representationalist (SR) theory of phenomenal consciousness pursues two projects. The first is to offer a positive account of how conscious experience arises from physical brain processes. The second is to explain why consciousness misleadingly appears to be irreducible to the physical i.e. to 'demystify' consciousness. This paper seeks to determine whether SR succeeds on the sec...

Let G be a complex reductive algebraic group and let Γ be a finitely generated group. In this paper we study properties of irreducible and completely reducible representations ρ : Γ → G in the context of the geometric invariant theory of the G-action on Hom(Γ, G) by conjugation. In particular, we prove that ρ is poly-stable (i.e. its orbit is closed) if and only if ρ is completely reducible. We...

Weyl’s character formula is a useful tool in understanding the structure of irreducible representations of semisimple Lie algebras. Even more important than the character formula itself is a corollary, the Weyl dimension formula, which gives a fairly simple expression for the total dimension of the representation in terms of the root system of the Lie algebra. Although the results discussed are...

In 1998, the second author raised the problem of classifying the irreducible characters of Sn of prime power degree. Zalesskii proposed the analogous problem for quasi-simple groups, and he has, in joint work with Malle, made substantial progress on this latter problem. With the exception of the alternating groups and their double covers, their work provides a complete solution. In this article...