Cuspidal representations of distinguished by a maximal Levi subgroup, with F a non-archimedean local field

2012 ◽  
Vol 350 (17-18) ◽  
pp. 797-800 ◽  
Author(s):  
Nadir Matringe
Keyword(s):  
Local Field ◽  
Levi Subgroup ◽  
Cuspidal Representations

scholarly journals Rankin–Selberg gamma factors of level zero representations of GLn

2019 ◽  
Vol 31 (2) ◽  
pp. 503-516 ◽  
Author(s):  
Rongqing Ye
Keyword(s):  
Local Field ◽  
Residue Field ◽  
Converse Theorem ◽  
Level Zero ◽  
Gamma Factor ◽  
Cuspidal Representations

AbstractFor a p-adic local field F of characteristic 0, with residue field {\mathfrak{f}}, we prove that the Rankin–Selberg gamma factor of a pair of level zero representations of linear general groups over F is equal to a gamma factor of a pair of corresponding cuspidal representations of linear general groups over {\mathfrak{f}}. Our results can be used to prove a variant of Jacquet’s conjecture on the local converse theorem.

Generic cuspidal representations of 𝑈(2, 1)

2021 ◽  
Vol 33 (3) ◽  
pp. 709-742
Author(s):  
Santosh Nadimpalli
Keyword(s):  
Local Field ◽  
Classical Groups ◽  
Fixed Field ◽  
Residue Characteristic ◽  
Cuspidal Representations

Abstract Let 𝐹 be a non-Archimedean local field, and let 𝜎 be a non-trivial Galois involution with fixed field F 0 F_{0} . When the residue characteristic of F 0 F_{0} is odd, using the construction of cuspidal representations of classical groups by Stevens, we classify generic cuspidal representations of U ⁢ ( 2 , 1 ) ⁢ ( F / F 0 ) U(2,1)(F/F_{0}) .

scholarly journals Multiplicity Free Jacquet Modules

2012 ◽  
Vol 55 (4) ◽  
pp. 673-688 ◽  
Author(s):  
Avraham Aizenbud ◽  
Dmitry Gourevitch
Keyword(s):  
Finite Field ◽  
Natural Number ◽  
Parabolic Subgroup ◽  
Local Field ◽  
Classical Method ◽  
Irreducible Representations ◽  
Levi Subgroup ◽  
Unipotent Subgroup ◽  
Multiplicity Free

AbstractLet F be a non-Archimedean local field or a finite field. Let n be a natural number and k be 1 or 2. Consider G := GLn+k(F) and let M := GLn(F) × GLk(F) < G be a maximal Levi subgroup. Let U < G be the corresponding unipotent subgroup and let P = MU be the corresponding parabolic subgroup. Let be the Jacquet functor, i.e., the functor of coinvariants with respect toU. In this paper we prove that J is a multiplicity free functor, i.e., dim HomM(J(π), ρ) ≤ 1, for any irreducible representations π of G and ρ of M. We adapt the classical method of Gelfand and Kazhdan, which proves the “multiplicity free” property of certain representations to prove the “multiplicity free” property of certain functors. At the end we discuss whether other Jacquet functors are multiplicity free.

scholarly journals Regular Bernstein blocks

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jeffrey D. Adler ◽  
Manish Mishra
Keyword(s):  
Local Field ◽  
Reductive Group ◽  
Levi Subgroup ◽  
Supercuspidal Representation ◽  
Category Of Smooth Representations ◽  
Residual Characteristic

Abstract For a connected reductive group G defined over a non-archimedean local field F, we consider the Bernstein blocks in the category of smooth representations of G ⁢ ( F ) {G(F)} . Bernstein blocks whose cuspidal support involves a regular supercuspidal representation are called regular Bernstein blocks. Most Bernstein blocks are regular when the residual characteristic of F is not too small. Under mild hypotheses on the residual characteristic, we show that the Bernstein center of a regular Bernstein block of G ⁢ ( F ) {G(F)} is isomorphic to the Bernstein center of a regular depth-zero Bernstein block of G 0 ⁢ ( F ) {G^{0}(F)} , where G 0 {G^{0}} is a certain twisted Levi subgroup of G. In some cases, we show that the blocks themselves are equivalent, and as a consequence we prove the ABPS Conjecture in some new cases.

scholarly journals Bernstein center of supercuspidal blocks

2019 ◽  
Vol 2019 (748) ◽  
pp. 297-304
Author(s):  
Manish Mishra
Keyword(s):  
Local Field ◽  
Reductive Group ◽  
Levi Subgroup

Abstract Let \mathbf{G} be a tamely ramified connected reductive group defined over a non-archimedean local field k. We show that the Bernstein center of a tame supercuspidal block of \mathbf{G}(k) is isomorphic to the Bernstein center of a depth-zero supercuspidal block of \mathbf{G}^{0}(k) for some twisted Levi subgroup of \mathbf{G}^{0} of \mathbf{G} .

scholarly journals Cuspidal ℓ-modular representations of p-adic classical groups

2020 ◽  
Vol 2020 (764) ◽  
pp. 23-69 ◽  
Author(s):  
Robert Kurinczuk ◽  
Shaun Stevens
Keyword(s):  
Local Field ◽  
Classical Group ◽  
Irreducible Representations ◽  
Closed Field ◽  
Modular Representations ◽  
Algebraically Closed Field ◽  
Fundamental Step ◽  
Residual Characteristic ◽  
Cuspidal Representations

AbstractFor a classical group over a non-archimedean local field of odd residual characteristic p, we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p, as representations induced from a cuspidal type. We also give a fundamental step towards the classification of cuspidal representations, identifying when certain cuspidal types induce to equivalent representations; this result is new even in the case of complex representations. Finally, we prove that the representations induced from more general types are quasi-projective, a crucial tool for extending the results here to arbitrary irreducible representations.

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