scholarly journals Parabolic induction and Jacquet functors for metaplectic groups

2010 ◽  
Vol 323 (1) ◽  
pp. 241-260 ◽  
Author(s):  
Marcela Hanzer ◽  
Goran Muić
Keyword(s):  
Metaplectic Groups ◽  
Parabolic Induction

scholarly journals Lifting of characters on p-adic orthogonal and metaplectic groups

2010 ◽  
Vol 146 (3) ◽  
pp. 795-810 ◽  
Author(s):  
Tatiana K. Howard
Keyword(s):  
Transfer Factor ◽  
Orthogonal Group ◽  
Symplectic Group ◽  
Dual Pair ◽  
Metaplectic Groups ◽  
Oscillator Representation ◽  
Parabolic Induction ◽  
The Difference ◽  
Metaplectic Cover ◽  
Split Orthogonal Group

AbstractLet F be a p-adic field. Consider a dual pair $({\rm SO}(2n+1)_+, \widetilde {{\rm Sp}}(2n)),$ where SO(2n+1)+ is the split orthogonal group and $\widetilde {{\rm Sp}}(2n)$ is the metaplectic cover of the symplectic group Sp(2n) over F. We study lifting of characters between orthogonal and metaplectic groups. We say that a representation of SO(2n+1)+ lifts to a representation of $\widetilde {{\rm Sp}}(2n)$ if their characters on corresponding conjugacy classes are equal up to a transfer factor. We study properties of this transfer factor, which is essentially the character of the difference of the two halves of the oscillator representation. We show that the lifting commutes with parabolic induction. These results were motivated by the paper ‘Lifting of characters on orthogonal and metaplectic groups’ by Adams who considered the case F=ℝ.

scholarly journals Metaplectic flavor symmetries from magnetized tori

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Yahya Almumin ◽  
Mu-Chun Chen ◽  
Víctor Knapp-Pérez ◽  
Saúl Ramos-Sánchez ◽  
Michael Ratz ◽  
...  
Keyword(s):  
Zero Mode ◽  
Metaplectic Groups ◽  
Common Multiple ◽  
Least Common Multiple ◽  
Yukawa Couplings ◽  
Flavor Symmetries ◽  
Euler’S Theorem ◽  
Modular Transformations ◽  
Analytic Expressions ◽  
Geometric Picture

Abstract We revisit the flavor symmetries arising from compactifications on tori with magnetic background fluxes. Using Euler’s Theorem, we derive closed form analytic expressions for the Yukawa couplings that are valid for arbitrary flux parameters. We discuss the modular transformations for even and odd units of magnetic flux, M, and show that they give rise to finite metaplectic groups the order of which is determined by the least common multiple of the number of zero-mode flavors involved. Unlike in models in which modular flavor symmetries are postulated, in this approach they derive from an underlying torus. This allows us to retain control over parameters, such as those governing the kinetic terms, that are free in the bottom-up approach, thus leading to an increased predictivity. In addition, the geometric picture allows us to understand the relative suppression of Yukawa couplings from their localization properties in the compact space. We also comment on the role supersymmetry plays in these constructions, and outline a path towards non-supersymmetric models with modular flavor symmetries.

scholarly journals On Reducibility and Unitarizability for Classical p-Adic Groups, Some General Results

2009 ◽  
Vol 61 (2) ◽  
pp. 427-450 ◽  
Author(s):  
Marko Tadić
Keyword(s):  
Reductive Groups ◽  
Parabolic Induction

Abstract. The aim of this paper is to prove two general results on parabolic induction of classical p-adic groups (actually, one of them holds also in the archimedean case), and to obtain from them some consequences about irreducible unitarizable representations. One of these consequences is a reduction of the unitarizability problem for these groups. This reduction is similar to the reduction of the unitarizability problem to the case of real infinitesimal character for real reductive groups.

scholarly journals Geometric approach to parabolic induction

2016 ◽  
Vol 22 (4) ◽  
pp. 2243-2269 ◽  
Author(s):  
David Kazhdan ◽  
Yakov Varshavsky
Keyword(s):  
Geometric Approach ◽  
Parabolic Induction

On the structure of the holomorphic representations of the noncompact symplectic and metaplectic groups

1994 ◽  
Vol 72 (7-8) ◽  
pp. 505-510 ◽  
Author(s):  
D. J. Rowe
Keyword(s):  
Harmonic Series ◽  
Metaplectic Groups

We review the properties of the holomorphic representations with lowest weights for the noncompact real symplectic and metaplectic groups. The unitarizable sub representations of these representations are identified with the harmonic series. We define unitary characters for the holomorphic representations and show how they can be used to identify the unitarizable sub quotient representations. Explicit results are given for Sp(1, R), Sp(2, R), and Sp(3, R).

scholarly journals Sur les -blocs de niveau zéro des groupes -adiques

2018 ◽  
Vol 154 (7) ◽  
pp. 1473-1507
Author(s):  
Thomas Lanard
Keyword(s):  
Abelian Category ◽  
Langlands Correspondence ◽  
Parabolic Induction ◽  
Langlands Parameters ◽  
Tits Building ◽  
Local Langlands Correspondence

Let $G$ be a $p$-adic group that splits over an unramified extension. We decompose $\text{Rep}_{\unicode[STIX]{x1D6EC}}^{0}(G)$, the abelian category of smooth level $0$ representations of $G$ with coefficients in $\unicode[STIX]{x1D6EC}=\overline{\mathbb{Q}}_{\ell }$ or $\overline{\mathbb{Z}}_{\ell }$, into a product of subcategories indexed by inertial Langlands parameters. We construct these categories via systems of idempotents on the Bruhat–Tits building and Deligne–Lusztig theory. Then, we prove compatibilities with parabolic induction and restriction functors and the local Langlands correspondence.

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