Relevant bibliographies by topics / Supercuspidal representation

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Academic literature on the topic 'Supercuspidal representation'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Supercuspidal representation"

1

Asmuth, Charles. "Some Supercuspidal Representations of Sp4(k)." Canadian Journal of Mathematics 39, no. 1 (1987): 1–7. http://dx.doi.org/10.4153/cjm-1987-001-9.

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The purpose of this paper is to produce explicit realizations of supercuspidal representations of Sp4(k) where k is a p-adic field with odd residual characteristic. These representations will be constructed using the Weil representation of Sp4(k) associated with a certain 4-dimensional compact orthogonal group OQ over k. The main problem addressed in this paper is the analysis of this representation; we need to find how the supercuspidal summands decompose into irreducible pieces.The problem of decomposing Weil representations has been studied quite a bit already. The Weil representations of S
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Valverde, Cesar. "On Induced Representations Distinguished by Orthogonal Groups." Canadian Mathematical Bulletin 56, no. 3 (2013): 647–58. http://dx.doi.org/10.4153/cmb-2012-008-0.

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Abstract.LetFbe a local non-archimedean field of characteristic zero. We prove that a representation ofGL(n,F) obtained from irreducible parabolic induction of supercuspidal representations is distinguished by an orthogonal group only if the inducing data is distinguished by appropriate orthogonal groups. As a corollary, we get that an irreducible representation induced from supercuspidals that is distinguished by an orthogonal group is metic.
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Savin, Gordan, and Martin H. Weissman. "Dichotomy for generic supercuspidal representations ofG2." Compositio Mathematica 147, no. 3 (2011): 735–83. http://dx.doi.org/10.1112/s0010437x10005178.

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AbstractThe local Langlands conjectures imply that to every generic supercuspidal irreducible representation ofG2over ap-adic field, one can associate a generic supercuspidal irreducible representation of either PGSp6or PGL3. We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations ofG2and other representations of PGSp6and PGL3. This correspondence arises from theta correspondences inE6andE7, analysis of Shalika functionals, and spin L-functions. Our main result reduces the conjectural Langlands parameterization of generic supercuspidal irredu
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Baruch, Ehud Moshe, and Kobi Snitz. "A Note on Bessel Functions for Supercuspidal Representations of GL(2) over a p-Adic Field." Algebra Colloquium 18, spec01 (2011): 733–38. http://dx.doi.org/10.1142/s1005386711000605.

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We compute the Bessel functions which give the action of the Weyl group element in the Kirillov model of supercuspidal representations of GL 2(K), where Kis a p-adic field. Together with the known action of the Borel subgroup, this gives the full action of GL 2(K) for such representations. We consider supercuspidal representations constructed by Jacquet and Langlands using the Weil representation. When the residual characteristic is odd, these are all the supercuspidal representations, hence we get a full description of all supercuspidal representations in this case.
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Hakim, Jeffrey, and Fiona Murnaghan. "Globalization of Distinguished Supercuspidal Representations of GL(n)." Canadian Mathematical Bulletin 45, no. 2 (2002): 220–30. http://dx.doi.org/10.4153/cmb-2002-025-x.

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AbstractAn irreducible supercuspidal representation π of G = GL(n, F), where F is a nonarchimedean local field of characteristic zero, is said to be “distinguished” by a subgroup H of G and a quasicharacter χ of H if HomH(π, χ) ≠ 0. There is a suitable global analogue of this notion for an irreducible, automorphic, cuspidal representation associated to GL(n). Under certain general hypotheses, it is shown in this paper that every distinguished, irreducible, supercuspidal representation may be realized as a local component of a distinguished, irreducible automorphic, cuspidal representation. App
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Blondel, Corinne, and Geo Kam-Fai Tam. "Base change for ramified unitary groups: The strongly ramified case." Journal für die reine und angewandte Mathematik (Crelles Journal) 2021, no. 774 (2021): 127–61. http://dx.doi.org/10.1515/crelle-2020-0049.

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Abstract We compute a special case of base change of certain supercuspidal representations from a ramified unitary group to a general linear group, both defined over a p-adic field of odd residual characteristic. In this special case, we require the given supercuspidal representation to contain a skew maximal simple stratum, and the field datum of this stratum to be of maximal degree, tamely ramified over the base field, and quadratic ramified over its subfield fixed by the Galois involution that defines the unitary group. The base change of this supercuspidal representation is described by a
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Ban, Dubravka. "Jacquet Modules of Parabolically Induced Representations and Weyl Groups." Canadian Journal of Mathematics 53, no. 4 (2001): 675–95. http://dx.doi.org/10.4153/cjm-2001-027-7.

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AbstractThe representation parabolically induced from an irreducible supercuspidal representation is considered. Irreducible components of Jacquet modules with respect to induction in stages are given. The results are used for consideration of generalized Steinberg representations.
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Murnaghan, Fiona. "Local Character Expansions for Supercuspidal Representations of U(3)." Canadian Journal of Mathematics 47, no. 3 (1995): 606–40. http://dx.doi.org/10.4153/cjm-1995-032-x.

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AbstractThe topic of this paper is the relationship between characters of irreducible supercuspidal representations of the p-adic unramified 3 x 3 unitary group and Fourier transforms of invariant measures on elliptic adjoint orbits in the Lie algebra. We prove that most supercuspidal representations have the property that, on some neighbourhood of zero, the character composed with the exponential map coincides with the formal degree of the representation times the Fourier transform of a measure on one elliptic orbit. For the remainder, a linear combination of the Fourier transforms of measure
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9

Morris, Lawrence. "Tamely ramified supercuspidal representations of classical groups. II. Representation theory." Annales scientifiques de l'École normale supérieure 25, no. 3 (1992): 233–74. http://dx.doi.org/10.24033/asens.1649.

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Savin, Gordan. "A Class of Supercuspidal Representations of G2(k)." Canadian Mathematical Bulletin 42, no. 3 (1999): 393–400. http://dx.doi.org/10.4153/cmb-1999-046-9.

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AbstractLet H be an exceptional, adjoint group of type E6 and split rank 2, over a p-adic field k. In this article we discuss the restriction of the minimal representation of H to a dual pair PD× × G2(k), where D is a division algebra of dimension 9 over k. In particular, we discover an interesting class of supercuspidal representations of G2(k).
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Dissertations / Theses on the topic "Supercuspidal representation"

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Mayeux, Arnaud. "On the constructions of supercuspidal representations." Thesis, Sorbonne Paris Cité, 2019. http://www.theses.fr/2019USPCC016.

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Nous commençons par comparer les constructions des représentations supercuspidales de Bushnell-Kutzko et Yu. Nous associons de manière explicite, sous une hypothèse nécessaire de modération, à chaque étape de la construction de Bushnell-Kutzko une partie d'une donnée de Yu. Nous obtenons ainsi finalement un lien entre les deux constructions dans le cas où les constructions sont toutes les deux définies: GLN dans une situation modérée. Dans une seconde partie, G désigne un groupe réductif connexe défini sur un corps p-adique k, nous définissons pour chaque point rationnel x dans l'immeuble de B
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Ye, Rongqing. "Explicit formulas for local factors of supercuspidal representations of $GL_n$ and their applications." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1558359289350258.

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Bourgeois, Adèle. "On the Restriction of Supercuspidal Representations: An In-Depth Exploration of the Data." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/40901.

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Let $\mathbb{G}$ be a connected reductive group defined over a p-adic field F which splits over a tamely ramified extension of F, and let G = $\mathbb{G}(F)$. We also assume that the residual characteristic of F does not divide the order of the Weyl group of $\mathbb{G}$. Following J.K. Yu's construction, the irreducible supercuspidal representation constructed from the G-datum $\Psi$ is denoted $\pi_G(\Psi)$. The datum $\Psi$ contains an irreducible depth-zero supercuspidal representation, which we refer to as the depth-zero part of the datum. Under our hypotheses, the J.K. Yu Constructio
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Almutairi, Bander Nasser. "Counting supercuspidal representations of p-adic groups." Thesis, University of East Anglia, 2012. https://ueaeprints.uea.ac.uk/48008/.

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Let F be a non-archimedean local �eld with residual characteristic p ~= 2. In this thesis we will deduce a formula for the number of irreducible supercuspidal representations of GLN(F), N C 1, with !�($F ) = 1 and level less than or equal to k. Following Blasco, we construct all irreducible supercuspidal representations of the unitary groups U(1; 1)(F~F0) and U(2; 1)(F~F0) by looking at their characteristic polynomials and then compute the number of all these representations according to their level.
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Paskunas, Vytautas. "Unicity of types for supercuspidal representations of GLn." Thesis, University of Nottingham, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.289454.

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Danisman, Yusuf. "L-factors of Supercuspidal Representations of p-adic GSp(4)." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1305777152.

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Cui, Peiyi. "Modulo l-representations of p-adic groups SL_n(F)." Thesis, Rennes 1, 2019. http://www.theses.fr/2019REN1S050/document.

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Fixons un nombre premier p. Soit k un corps algébriquement clos de caractéristique l différent que p. Nous construisons les k-types maximaux simples cuspidaux des sous-groupes de Levi M' de SL_n(F), où F est un corps local non archimédien de caractéristique résiduelle p. Nous montrons que le support supercuspidal des k-représentations lisses irréductibles de M' est unique à M'-conjugaison près, quand F est soit un corps fini de caractéristique p soit un corps local non-archimédien de caractéristique résiduelle p<br>Fix a prime number p. Let k be an algebraically closed field of characteristic
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Klupsch, Matthias Verfasser], Gerhard [Akademischer Betreuer] Hiß, Meinolf [Akademischer Betreuer] Geck, and Gabriele [Akademischer Betreuer] [Nebe. "On cuspidal and supercuspidal representations of finite reductive groups / Matthias Klupsch ; Gerhard Hiß, Meinolf Geck, Gabriele Nebe." Aachen : Universitätsbibliothek der RWTH Aachen, 2016. http://d-nb.info/1130402908/34.

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Klupsch, Matthias [Verfasser], Gerhard Akademischer Betreuer] Hiß, Meinolf [Akademischer Betreuer] Geck, and Gabriele [Akademischer Betreuer] [Nebe. "On cuspidal and supercuspidal representations of finite reductive groups / Matthias Klupsch ; Gerhard Hiß, Meinolf Geck, Gabriele Nebe." Aachen : Universitätsbibliothek der RWTH Aachen, 2016. http://d-nb.info/1130402908/34.

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Boller, John David. "Characters of some supercuspidal representations of p-ADIC Sp[subscrip]4(F) /." 1999. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:9951766.

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Books on the topic "Supercuspidal representation"

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Blondel, Corinne. Les représentations supercuspidales des groupes métaplectiques sur GL[2] et leurs caractères: Par Corinne Blondel. Gauthier-Villars, 1985.

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Jabon, David. The supercuspidal representations of U(2,1) and GSP₄ over a local field via Hecke algebra isomorphisms. 1989.

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Book chapters on the topic "Supercuspidal representation"

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Reeder, Mark. "Some New Supercuspidal Representations." In Representation Theory, Number Theory, and Invariant Theory. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59728-7_17.

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Adrian, Moshe. "The Character of a Simple Supercuspidal Representation of SL(2, F)." In Progress in Mathematics. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6628-4_4.

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Corwin, Lawrence. "Constructing the Supercuspidal Representation of GL n (F), F p—ADIC." In Progress in Mathematics. Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0455-8_7.

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Kim, Ju-Lee. "Supercuspidal representations: Construction and exhaustion". У Ottawa Lectures on Admissible Representations of Reductive 𝑝-adic Groups. American Mathematical Society, 2009. http://dx.doi.org/10.1090/fim/026/03.

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Hakim, Jeffrey. "Supercuspidal representations and symmetric spaces." In Algebra and Number Theory. Hindustan Book Agency, 2005. http://dx.doi.org/10.1007/978-93-86279-23-1_16.

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Latham, Peter, and Monica Nevins. "On the Unicity of Types for Toral Supercuspidal Representations." In Progress in Mathematics. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6628-4_6.

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"Non-supercuspidal Representations." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-73324-9_5.

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