On Newforms for Split Special Odd Orthogonal Groups
Contributors: Gross, Benedict H.; Gross, Benedict H.; Mazur, Barry; Schmid, Wilfried
Published: 2013
Language: eng
Description: The theory of local newforms has been studied for the group of PGL(n) and recently PGSp(4) and some other groups of small ranks. In this dissertation, we develop a newform theory for generic supercuspidal representations of SO(2n+1) over non-Archimedean local fields with odd characteristic by defining a family of open compact subgroup K(p m), m ≥ 0 (up to conjugacy) which are analogous to the groups Γ_0(p m) in the classical theory of modular forms. We give lower bounds on the dimension of the fixed subspaces of K(p m) in terms of the conductor of the generic representation, and give a conjectural description of the space of old forms. These results generalize the known cases for n = 1,2 by Casselman [4] and Roberts and Schmidt [23].
Notes: Keywords: conductor, congruence subgroups, multiplicity one, newform, oldform, SO(2n+1).

Thesis Ph.D. Harvard University 2013