In this chapter we study an example of a multiplicity-free triple where the representation that we induce has dimension greater than one. Let q = ph with p an odd prime and h ≥ 1. Set (formula presented) the Borel (resp. the unipotent, resp. the Cartan) subgroup of Gj, for j = 1, 2. Throughout this chapter, with the notation as in Sect. 5.3, we let (formula presented) be a fixed indecomposable character. We assume that (formula presented) is not a square: this slightly simplifies the decomposition into irreducibles. Finally, ρν denotes the cuspidal representation of G1 associated with ν.
In questo capitolo studiamo una seconda terna priva di molteplicità ottenuta tramite gruppi lineari su campi finiti. La particolarità è che si induce una rappresentazione di dimensione maggiore di 1.
Harmonic analysis of the multiplicity-free triple (gl(2,Fq2),GL(2,Fq),ρν) / Ceccherini-Silberstein, T.; Scarabotti, F.; Tolli, F.. - (2020), pp. 95-119. - LECTURE NOTES IN MATHEMATICS. [10.1007/978-3-030-51607-9_6].
Harmonic analysis of the multiplicity-free triple (gl(2,Fq2),GL(2,Fq),ρν)
Scarabotti F.;
2020
Abstract
In this chapter we study an example of a multiplicity-free triple where the representation that we induce has dimension greater than one. Let q = ph with p an odd prime and h ≥ 1. Set (formula presented) the Borel (resp. the unipotent, resp. the Cartan) subgroup of Gj, for j = 1, 2. Throughout this chapter, with the notation as in Sect. 5.3, we let (formula presented) be a fixed indecomposable character. We assume that (formula presented) is not a square: this slightly simplifies the decomposition into irreducibles. Finally, ρν denotes the cuspidal representation of G1 associated with ν.| File | Dimensione | Formato | |
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Ceccherini-Silberstein_Representation_2014.pdf
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