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On Schur multiplier and projective representations of Heisenberg groups. (English) Zbl 1483.20027

The theory of projective representations involves understanding homomorphisms from a group into the projective linear groups. By definition, every ordinary representation of a group is projective, but the converse is not true.
The Schur multiplier of a group \(G\) is the second cohomology group \(\mathrm{H}^2(G, \mathbb{C}^{\times})\), where \(\mathbb{C}^{\times}\) is a trivial \(G\)-module and, for that, it is a useful tool to understanding projective representations.
In the paper under review, the authors describe the Schur multiplier, the representation of discrete Heisenberg groups and their \(t\)-variants. Furthermore, they provide a construction of all complex finite dimensional irreducible projective representations of these groups.

MSC:

20C25 Projective representations and multipliers
20G05 Representation theory for linear algebraic groups
20F18 Nilpotent groups
20J06 Cohomology of groups
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