Singer torus in irreducible representations of GL(n,q)
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Alexandre E. Zalesski
Abstract
Let G = PGL(n,q) be the projective general linear group of degree n over a finite field of q elements. Let T be a Singer torus of G, that is, a maximal torus of G of order |T| = (qn-1)/(q-1). Let χ be an irreducible character of G. We prove that the trivial character 1T of T occurs as a constituent of the restriction of χ to T unless χ(1) < |T|. This answers a question raised by Pablo Spiga.
I am grateful to Pham Huu Tiep for sending me his manuscript [9] before publication and to the referee for a new proof of Proposition 3.1, which is much simpler than the original one.
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© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Sliceable groups and towers of fields
- Pro-Hall R-groups and groups discriminated by the free pro-p group
- Filtrations of free groups arising from the lower central series
- Prosolvability criteria and properties of the prosolvable radical via Sylow sequences
- Non-commutative lattice problems
- Conjugacy distinguished subgroups
- Diophantine questions in the class of finitely generated nilpotent groups
- Uncountably many non-commensurable finitely presented pro-p groups
- Singer torus in irreducible representations of GL(n,q)
- Virtually free pro-p products
Articles in the same Issue
- Frontmatter
- Sliceable groups and towers of fields
- Pro-Hall R-groups and groups discriminated by the free pro-p group
- Filtrations of free groups arising from the lower central series
- Prosolvability criteria and properties of the prosolvable radical via Sylow sequences
- Non-commutative lattice problems
- Conjugacy distinguished subgroups
- Diophantine questions in the class of finitely generated nilpotent groups
- Uncountably many non-commensurable finitely presented pro-p groups
- Singer torus in irreducible representations of GL(n,q)
- Virtually free pro-p products
