Conductors and newforms for SL(2)

Lansky, Joshua M.; Raghuram, A.

doi:10.2140/pjm.2007.231.127

Cited by 10 publications

(13 citation statements)

References 21 publications

(25 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We would also like to signal the closely related work of J. Lansky and A. Raghuram [16], whose focus is the determination of newforms for SL 2 (k); this amounts to identifying and characterizing the irreducible component of least depth (and least degree) occuring in the restriction of a representation of SL 2 (k) to a maximal compact subgroup.…”

Section: Introductionmentioning

confidence: 99%

Branching Rules for Principal Series Representations of SL(2) over a p-adic Field

Nevins¹

2005

Can. j. math.

View full text Add to dashboard Cite

Abstract. We explicitly describe the decomposition into irreducibles of the restriction of the principal series representations of SL(2, k), for k a p-adic field, to each of its two maximal compact subgroups (up to conjugacy). We identify these irreducible subrepresentations in the Kirillov-type classification of Shalika. We go on to explicitly describe the decomposition of the reducible principal series of SL (2, k) in terms of the restrictions of its irreducible constituents to a maximal compact subgroup.

show abstract

Section: Introductionmentioning

confidence: 99%

Branching Rules for Principal Series Representations of SL(2) over a p-adic Field

Nevins¹

2005

Can. j. math.

View full text Add to dashboard Cite

show abstract

“…2 ). By Proposition 3.2.4 of [17] we have that dim( π SL 2 (O Fv ) ) = 1. We denote the unique member of the L-packet of π that has a non-zero SL 2 (O Fv )-fixed vector by π 0 and in a global context by π 0 v .…”

Section: 1mentioning

confidence: 88%

“…the refinements agree when restricted to Σ + . Furthermore dim τ I 1 = dim τ I 2 = 1 (see Proposition 3.2.12 of [17]), so each member of the L-packet sees the same eigenvalues. This implies that in the proof of the previous proposition there is in fact no need to change the representation at p. Proposition 5.6.…”

Section: 3mentioning

confidence: 98%

A p-adic Labesse–Langlands transfer

Ludwig

2017

manuscripta math.

View full text Add to dashboard Cite

Abstract. We prove a p-adic Labesse-Langlands transfer from the group of units in a definite quaternion algebra to its subgroup of norm one elements. More precisely, given an eigenvariety for the first group, we show that there exists an eigenvariety for the second group and a morphism between them that extends the classical Langlands transfer. In order to find a suitable target eigenvariety for the transfer we formalise a notion of Langlands compatibility of tame levels. Proving the existence of Langlands compatible tame levels is the key to pass from the classical transfer on the level of L-packets to a map between classical points of eigenvarieties, which is then amenable for interpolation to give the p-adic transfer.

show abstract

“…One has to distinguish between two kinds of such L-packets. The first kind (called unramified supercuspidal L-packet in [15]) is given by representations π that are compactly induced from a representation σ of Z GL 2 (Z l ). Here Z denotes the center of GL 2 (Q l ).…”

Section: Here a Representationmentioning

confidence: 99%

“…Here Z denotes the center of GL 2 (Q l ). The second kind (called ramified supercuspidal L-packet in [15]) is given by representations π that are compactly induced from the normalizer N GL 2 (Q l ) I of the standard Iwahori I of GL 2 (Q l ) of upper triangular matrices mod l. Supercuspidal L-packets of the second kind are always of size two, those of the first kind can be of size four, namely when the representation σ is of level one in the sense of Definition 3.3.1 in [15]. But when this level is greater than or equal to two, the resulting L-packet is of size two.…”

Section: Here a Representationmentioning

confidence: 99%