Howe Correspondence of Unipotent Characters for a Finite Symplectic/Even-orthogonal Dual Pair

Pan, Shu-Yen

doi:10.48550/arxiv.1901.00623

Cited by 10 publications

(17 citation statements)

References 14 publications

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“…The following proposition is a modification for O ǫ 2n (q) from [Lus82] theorem 3.15 (cf. [Pan19a] proposition 3.19): Proposition 2.12 (Lusztig). Let Z be a non-degenerate special symbol of defect 0 and degree d ≥ 1.…”

Section: Symbols and Unipotent Charactersmentioning

confidence: 97%

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Lusztig Correspondence and Howe Correspondence for Finite Reductive Dual Pairs

Pan¹

2019

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Let (G, G ′ ) be a finite reductive dual pair of a symplectic group and an orthogonal group. The Howe correspondence establishes a correspondence between a subset of irreducible characters of G and a subset of irreducible characters of G ′ . The Lusztig correspondence is a bijection between the Lusztig series indexed by the conjugacy class of a semisimple element s in the connected component (G * ) 0 of the dual group of G and the set of irreducible unipotent characters of the centralizer of s in G * . In this paper, we prove the commutativity (up to a twist of the sign character) between these two correspondences under some restriction on the characteristic of the finite field.

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Section: Symbols and Unipotent Charactersmentioning

confidence: 97%

“…[AM93]). Moreover, the explicit description of the Howe correspondence of irreducible unipotent characters in terms of combinatorial parameters is in [AMR96] for unitary dual pairs and in [Pan19a] for symplectic/evenorthogonal dual pairs. Now we recall these results briefly in the following.…”

Section: Introductionmentioning

confidence: 99%

Lusztig Correspondence and Howe Correspondence for Finite Reductive Dual Pairs

Pan¹

2019

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“…[AM93] theorem 3.5). The following result on the Θ-correspondence of unipotent characters is from [Pan19a] Then from (2.5) we can write…”

Section: Unipotent Characters Of Symplectic or Orthogonal Groupsmentioning

confidence: 99%

Degree Differences in the Eta Correspondences

Pan¹

2021

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A sub-relation of the Θ-correspondence called the η-correspondence is defined by Gurevich-Howe for a finite reductive dual pair in stable range.In this paper we propose an extension of the correspondence to general finite reductive dual pairs. Then we determine the domain the correspondence and prove a formula on the difference of degrees in q of two irreducible characters paired by the correspondence.

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“…There are two types of periods in the Gan-Gross-Prasad conjecture: the Bessel periods and the Fourier-Jacobi periods and we can deduce the Fourier-Jacobi case from the Bessel case by the standard arguments of theta correspondence and see-saw dual pairs, which are used in the proof of local Gan-Gross-Prasad conjecture (see [GI, Ato]). A complete understanding of theta correspondence over finite fields is known in [AMR,P1,P2] and theta correspondence for the representations considering in this paper is quite simple. So in this paper, we only focus on the Bessel case.…”

Section: Introductionmentioning

confidence: 99%