Example 1.2. The trivial character of G is the homomorphism 1G defined by 1G(g) = 1 for all g ∈ G. Example 1.3. Let G be cyclic of order 4 with generator γ. Since γ4 = 1, a character χ of G has χ(γ)4 = 1, so χ takes only four possible values at γ, namely 1, −1, i, or −i. Once χ(γ) is known, the value of χ elsewhere is determined by multiplicativity: χ(γj) = χ(γ)j . So we get four characters, wh...

the full automorphism group of $u_6(2)$ is a group of the form $u_6(2){:}s_3$. the group $u_6(2){:}s_3$ has a maximal subgroup $2^9{:}(l_3(4){:}s_3)$ of order 61931520. in the present paper, we determine the fischer-clifford matrices (which are not known yet) and hence compute the character table of the split extension $2^9{:}(l_3(4){:}s_3)$.

We call a finite group metabelian if its commutator subgroup is abelian. Thus a split metabelian group is a split extension of one abelian group by a second (possibly trivial) abelian group. In this paper we devise an algorithm for the construction of the character table of any split metabelian group G. The only requisites are that the reader be capable of deriving the character table for an ab...

We determine the 2-modular character table of the third sporadic simple group of Conway, up to two ambiguities. In each of these cases we give the smallest possibility for the character, which is also very likely to be the correct answer.

In this paper, we show that integral fusion categories with rational structure constants admit a natural group of symmetries given by the Galois their character tables. Based on these symmetries, generalize well-known result Burnside from representation theory finite groups. More precisely, any row corresponding to non-invertible object in table weakly category contains zero entry.

We propose a general conjecture for the mixed Hodge polynomial of the generic character varieties of representations of the fundamental group of a Riemann surface of genus g to GLn.C/ with fixed generic semisimple conjugacy classes at k punctures. This conjecture generalizes the Cauchy identity for Macdonald polynomials and is a common generalization of two formulas that we prove in this paper....

This research aimed to explore and describe the types of conflict that occurred in ParaNorman Movie. object was movie, specifically its main character Norman Babcock. The instruments consisted observation protocol documentation. Data collection through eight necessary steps, namely, 1) watch 2) download script, 3) make sure script movie were line, 4) observe conflicts, 5) identify conflict, 6) ...

Document images undergo various degradation processes. Numerous models of these degradation processes have been proposed in the literature. In this paper we propose a model-based restoration algorithm. The restoration algorithm rst estimates the parameters of a degradation model and then uses the estimated parameters to construct a lookup table for restoring the degraded image. The estimated de...

In the high rank limit, fraction of non-zero character table entries finite simple groups Lie type goes to zero.