The unitary dual of Gl (3, ?) and Gl (4, ?)

Speh, Birgit

doi:10.1007/bf01450529

Cited by 38 publications

(24 citation statements)

References 5 publications

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“…at split non-archimedean, Theorem B.2.d of [8] at non-split and results of [47] at archimedean places, the induced representation is irreducible. Hence, the normalized operator acts as ±Id v .…”

Section: So4(kv )mentioning

confidence: 97%

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On the residual spectrum of Hermitian quaternionic inner form of SO_8

Grbac¹

2009

Glas. Mat. Ser. III

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Abstract. In this paper we decompose the residual spectrum supported in the minimal parabolic subgroup of an inner form of the split group SO 8 . The approach is the Langlands spectral theory. However, since the group is non-quasi-split, it is out of the scope of the Langlands-Shahidi method and the new technique for the normalization of standard intertwining operators is developed. The decomposition shows interesting parts of the residual spectrum not appearing in the case of quasi-split groups.

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Section: So4(kv )mentioning

confidence: 97%

“…Before giving the decomposition of the space L 2 A3 we give a few facts concerning the induced representation Ind [8] at non-split and results of [47] at archimedean places, the induced representation above is irreducible and hence the normalized operator…”

Section: So4(kv )mentioning

confidence: 99%

On the residual spectrum of Hermitian quaternionic inner form of SO_8

Grbac¹

2009

Glas. Mat. Ser. III

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“…By the construction of the test function in [6], p. 903, this implies that the contribution of π is zero. Therefore, by the classification of the unitary dual in [19], it remains to consider the case of the trivial representation and the case when π is unitarily induced from P = MAN. So let π = π ξ,ν be induced from P , where ν is imaginary.…”

Section: + Ir)mentioning

confidence: 99%

Class Numbers of Orders in Cubic Fields

Deitmar

2002

Journal of Number Theory

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Abstract. In this paper it is shown that the sum of class numbers of orders in complex cubic fields obeys an asymptotic law similar to the prime numbers as the bound on the regulators tends to infinity. Here only orders are considered which are maximal at two given primes. This result extends work of P. Sarnak in the real quadratic case. It seems to be the first asymptotic result on class numbers for number fields of degree higher than two.

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“…For the last claim when verifying the surjectivity of the appropriate w of Lemma 2.2.1, one uses the irreducibility of certain induced representations for GL 3 (k v ) and GL 4 (k v ). These are given in [37] and [33]. Proof.…”

Section: Generic Representation At a Split Placementioning

confidence: 99%

“…Since the induced representation is irreducible by [34], [2], and [33], the normalized intertwining operator acts as Id or −Id. We denote the sign by η v .…”

Section: Before Passing To Lmentioning

confidence: 99%

The residual spectrum of an inner form of 𝑆𝑝₈ supported in the minimal parabolic subgroup

Grbac

2009

Trans. Amer. Math. Soc.

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Abstract. The part of the residual spectrum of an inner form of the split group Sp 8 supported in the minimal parabolic subgroup is decomposed. Since the considered inner form is not quasi-split, the normalization of the standard intertwining operators, required for the calculation of the poles of the Eisenstein series, is out of the reach of the Langlands-Shahidi method. Hence, a normalization technique, based on the transfer of the Plancherel measure between the split group and its inner form, is applied. The obtained decomposition reveals certain features of the residual spectrum of the inner form which do not appear for the split group.

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The unitary dual of Gl (3, ?) and Gl (4, ?)

Cited by 38 publications

References 5 publications

On the residual spectrum of Hermitian quaternionic inner form of SO_8

On the residual spectrum of Hermitian quaternionic inner form of SO_8

Class Numbers of Orders in Cubic Fields

The residual spectrum of an inner form of 𝑆𝑝₈ supported in the minimal parabolic subgroup

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