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.
2020-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
