Irreducible projective representations of finite groups

Tappe, Jürgen

doi:10.1007/bf01182065

Cited by 8 publications

(4 citation statements)

References 2 publications

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“…Using Corollary 7.6, we will deduce a key finiteness result for projective unitary representations of finite groups. This will be a corollary of the following classical result due to Schur [29] (see also Karpilovsky [10], Tappe [37,Corollary 3.6]).…”

Section: Now Any Projective Representationmentioning

confidence: 69%

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Periodicity in the stable representation theory of crystallographic groups

Ramras

2014

Forum Mathematicum

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Abstract. Deformation K-theory associates to each discrete group G a spectrum built from spaces of finite dimensional unitary representations of G. In all known examples, this spectrum is 2-periodic above the rational cohomological dimension of G (minus 2), in the sense that T. Lawson's Bott map is an isomorphism on homotopy in these dimensions. We establish a periodicity theorem for crystallographic subgroups of the isometries of k-dimensional Euclidean space. For a certain subclass of torsion-free crystallographic groups, we prove a vanishing result for the homotopy groups of the stable moduli space of representations, and we provide examples relating these homotopy groups to the cohomology of G.These results are established as corollaries of the fact that for each n > 0, the one-point compactification of the moduli space of irreducible n-dimensional representations of G is a CW complex of dimension at most k. This is proven using real algebraic geometry and projective representation theory.

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Section: Now Any Projective Representationmentioning

confidence: 69%

“…In fact, the set of such isomorphism classes is in bijection with the set of so-called σ-regular conjugacy classes in G [10, Theorem 6.7]. (An extension of this result can be found in Tappe [37].) We now conclude that there are finitely many ≈ GL -classes of irreducible projective representations with cocycle σ.…”

Section: Projective Representationsmentioning

confidence: 70%

Periodicity in the stable representation theory of crystallographic groups

Ramras

2014

Forum Mathematicum

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“…The results we will use to prove the theorem are in [44,59,60]. Let begin recalling that a theorem by Schur states that for every finite group Γ there exists a representation group H and A ≤ Z(H), such that Γ ∼ = H/A and A ≤ H ′ = [H, H] and A ∼ = H 2 (Γ, C * ).…”

Section: A Proof Of Theoremmentioning

confidence: 99%

Aspects of ABJM orbifolds with discrete torsion

Romo

2011

J. High Energ. Phys.

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We analyze orbifolds with discrete torsion of the ABJM theory by a finite subgroup Γ of SU(2) × SU(2) . Discrete torsion is implemented by twisting the crossed product algebra resulting after orbifolding. It is shown that, in general, the order m of the cocycle we chose to twist the algebra by enters in a non trivial way in the moduli space. To be precise, the M-theory fiber is multiplied by a factor of m in addition to the other effects that were found before in the literature. Therefore we got a Zk|Γ| m action on the fiber. We present a general analysis on how this quotient arises along with a detailed analysis of the cases where Γ is abelian.

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“…The character group Q acts on the set of irreducible characters Irr G by tensoring, and it is well known that (see e.g. [4,Thm 1.3]) #(conjugacy classes of G inside N ) = #( Q-orbits on Irr G). In this note, we give a simple representation-theoretic interpretation of conjugacy classes in other cosets of N , and discuss some corollaries.…”

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confidence: 99%

Character formula for conjugacy classes in a coset

Dokchitser,

Dokchitser

2021

Preprint

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Let G be a finite group and N ⊳ G a normal subgroup with G/N abelian. We show how the conjugacy classes of G in a given coset qN relate to the irreducible characters of G that are not identically 0 on qN . We describe several consequences. In particular, we deduce that when G/N is cyclic generated by q, the number of irreducible characters of N that extend to G is the number of conjugacy classes of G in qN .

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Irreducible projective representations of finite groups

Cited by 8 publications

References 2 publications

Periodicity in the stable representation theory of crystallographic groups

Periodicity in the stable representation theory of crystallographic groups

Aspects of ABJM orbifolds with discrete torsion

Character formula for conjugacy classes in a coset

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