Howe duality and dichotomy for exceptional theta correspondences

DOI10.1007/S00222-022-01165-2OpenAlexW3126295124MaRDI QIDQ2689657

Gordan Savin, Gan, Wee Teck

Publication date: 13 March 2023

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.00372

zbMATH Keywords

dichotomyHowe dualityexceptional group \(G_2\)exceptional theta correspondence

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (2)

The Local Langlands Conjecture for ⋮ A local Langlands parameterization for generic supercuspidal representations of $p$-adic $G_2$

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Matching of Hecke operators for exceptional dual pair correspondences
• Twisted Bhargava cubes
• The local Langlands conjecture for \(\text{GSp}(4)\)
• CAP representations of \(G_{2}\) and the spin \(L\)-function of \(\mathrm{PGSp}_6\)
• On the local theta-correspondence
• Modèles de Whittaker dégénéres pour des groupes p-adiques. (Degenerate Whittaker models of p-adic groups)
• Howe correspondences on a \(p\)-adic field
• Twisted endoscopy and reducibility of induced representations for \(p\)- adic groups
• The unitary dual of \(p\)-adic \(G_2\)
• Euler-Poincaré characteristic for the oscillator representation
• Degenerate principal series representations for quaternionic unitary groups
• A proof of Langlands' conjecture on Plancherel measures; complementary series for \(p\)-adic groups
• The theta correspondence for similitudes
• On minimal representations of Chevalley groups of type \(D_n\), \(E_n\) and \(G_{2}\)
• On a result of Moeglin and Waldspurger in residual characteristic 2
• A proof of the Howe duality conjecture
• Dichotomy for generic supercuspidal representations ofG₂
• Nontempered A-packets of G 2: Liftings from SL 2
• Correspondance de Howe explicite : paires duales de type II
• The Dual Pair G₂ × PU₃ (D) (p-Adic Case)
• A Class of Supercuspidal Representations of G₂(k)
• The Dual Pair PGL₃ × G₂
• Endoscopic lifts from PGL3 to G2
• Generalizing the MVW involution, and the contragredient
• The degenerate residual spectrum of quasi-split forms of $Spin_8$ associated to the Heisenberg parabolic subgroup
• Conservation relations for local theta correspondence
• A Künneth Theorem for p-Adic Groups
• Raising nilpotent orbits in wave-front sets
• Theta dichotomy for unitary groups
• Periods and liftings: From \(G_2\) to \(C_3\)

This page was built for publication: Howe duality and dichotomy for exceptional theta correspondences