On some representations of the Iwahori subgroup

Morra, Stefano

doi:10.1016/j.jnt.2011.11.002

Cited by 13 publications

(21 citation statements)

References 14 publications

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“…The second structure theorem clarifies a result already appearing in [Mo5] (Proposition 3.5) and is concerned with the N -restriction of the universal representation π(σ, 0). We remark that if F = Q p , this is a result of Paskunas ([Pas2], Theorem 6.3 and Corollary 6.5).…”

Section: Introductionmentioning

confidence: 60%

“…From the explicit description of the Hecke operator T one sees (cf. [Mo5], §2.2.1) that Im(T n ) is a sub-object of R n+1 ⊕ R n−1 , and we can consider the composition with the canonical the projections…”

Section: Each Direct Summand Is a K[i]-modulementioning

confidence: 99%

“…In particular, R − ∞,0 , R − ∞,−1 are not admissible unless F = Q p . A first study of R − ∞,0 , R − ∞,−1 had been pursued by the author in [Mo5] (by representation theoretic methods) and in [Mo6], [Mo7] (using methods from Iwasawa theory).…”

Section: Introductionmentioning

confidence: 99%

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Invariant elements for $p$-modular representations of ${\mathbf {GL}}_{2}({\mathbf {Q}}_p)$

Morra

2013

Trans. Amer. Math. Soc.

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Let p be an odd rational prime and F a p-adic field. We give a realization of the universal p-modular representations of GL 2 (F) in terms of an explicit Iwasawa module. We specialize our constructions to the case F = Q p , giving a detailed description of the invariants under principal congruence subgroups of irreducible admissible p-modular representations of GL 2 (Q p), generalizing previous work of Breuil and Paskunas. We apply these results to the local-global compatibility of Emerton, giving a generalization of the classical multiplicity one results for the Jacobians of modular curves with arbitrary level at p. Contents 1. Introduction 6625 1.1. Notation 6630 2. Reminders on the universal representations for GL 2 6633 2.1. Construction of the universal representation 6633 3. Structure theorems for universal representations 6637 3.1. Refinement of the Iwahori structure 6637 3.2. The case F = Q p 6647 4. Study of K t and I t invariants 6649 4.1. Invariants for the Iwasawa modules R − ∞,• 6649 4.2. Invariants for supersingular representations 6656 5. The case of principal and special series 6660 6. Global applications 6663 Acknowledgements 6665 References 6666

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Section: Introductionmentioning

confidence: 60%

Section: Each Direct Summand Is a K[i]-modulementioning

confidence: 99%

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Invariant elements for $p$-modular representations of ${\mathbf {GL}}_{2}({\mathbf {Q}}_p)$

Morra

2013

Trans. Amer. Math. Soc.

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“…We would like to emphasise that the previous results can be generalised without much effort to any finite extension of Q p , see [Mo2].…”

Section: Strategy Of the Proofmentioning

confidence: 85%

“…We stress out that the techniques of this paper can be generalised to unramified extensions of Q p , giving the Iwahori structure for the canonical Hecke operators in terms of euclidean structures (see [Mo2]). As a byproduct, we give the GL 2 (Z p )-socle filtration for unramified principal series.…”

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confidence: 99%

Explicit description of irreducible GL2(Qp)-representations over
Morra
¹

2011
Journal of Algebra
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Let p be an odd prime number. The classification of irreducible representations of GL 2 (Q p ) over F p is known thanks to the works of Barthel and Livné (1995) [BL95] and Breuil (2003) [Bre03a]. In the present paper we illustrate an exhaustive description of such irreducible representations, through the study of certain functions on the Bruhat-Tits tree of GL 2 (Q p ). In particular, we are able to detect the socle filtration for the K Z-restriction of supersingular representations, principal series and special series.

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Multiplicity theorems modulo $$p$$ p for $$\mathbf{GL }_{2}({\mathbf{Q}}_p)$$ GL 2 ( Q p )

Morra

2013

Math. Z.

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On some representations of the Iwahori subgroup

Cited by 13 publications

References 14 publications

Invariant elements for $p$-modular representations of ${\mathbf {GL}}_{2}({\mathbf {Q}}_p)$

Invariant elements for $p$-modular representations of ${\mathbf {GL}}_{2}({\mathbf {Q}}_p)$

Explicit description of irreducible GL2(Qp)-representations over
Morra
¹

2011
Journal of Algebra
Self Cite

Multiplicity theorems modulo $$p$$ p for $$\mathbf{GL }_{2}({\mathbf{Q}}_p)$$ GL 2 ( Q p )

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On some representations of the Iwahori subgroup

Cited by 13 publications

References 14 publications

Invariant elements for $p$-modular representations of ${\mathbf {GL}}_{2}({\mathbf {Q}}_p)$

Invariant elements for $p$-modular representations of ${\mathbf {GL}}_{2}({\mathbf {Q}}_p)$

Explicit description of irreducible GL2(Qp)-representations over Morra1 2011Journal of AlgebraSelf Cite

Multiplicity theorems modulo $$p$$ p for $$\mathbf{GL }_{2}({\mathbf{Q}}_p)$$ GL 2 ( Q p )

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About

Explicit description of irreducible GL2(Qp)-representations over
Morra
¹

2011
Journal of Algebra
Self Cite