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.

Ceccherini-Silberstein, T., Scarabotti, F., & Tolli, F. (2020). Harmonic analysis of the multiplicity-free triple (gl(2,Fq2),GL(2,Fq),ρν). In Lecture Notes in Mathematics (pp. 95-119). GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND : Springer Science and Business Media Deutschland GmbH [10.1007/978-3-030-51607-9_6].

Harmonic analysis of the multiplicity-free triple (gl(2,Fq2),GL(2,Fq),ρν)

Tolli 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.
978-3-030-51606-2
Ceccherini-Silberstein, T., Scarabotti, F., & Tolli, F. (2020). Harmonic analysis of the multiplicity-free triple (gl(2,Fq2),GL(2,Fq),ρν). In Lecture Notes in Mathematics (pp. 95-119). GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND : Springer Science and Business Media Deutschland GmbH [10.1007/978-3-030-51607-9_6].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/379199
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