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Waldspurger's Involution and Types
Author(s) -
Manderscheid David
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610704005721
Subject(s) - involution (esoterism) , quadratic equation , mathematics , pure mathematics , norm (philosophy) , character (mathematics) , combinatorics , geometry , philosophy , epistemology , consciousness
Waldspurger's involution for the genuine irreducible supercuspidal representations of SL 2 ( F ) is parametrized in terms of types in the case F p ‐adic with p odd. In particular, it is shown that the in‐volution is given by conjugating by an element of GL 2 ( F ) and twisting one of the defining parameters of an associated type by a quadratic character, the relevant parameter being a character on the norm one elements of a quadratic extension.