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 \(K(p^m)\), \(m \geq 0\) (up to conjugacy) which are analogous to the groups \(\Gamma(p^m)\) 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]. / Mathematics
| Identifer | oai:union.ndltd.org:harvard.edu/oai:dash.harvard.edu:1/11051219 |
| Date | 18 September 2013 |
| Creators | Tsai, Pei-Yu |
| Contributors | Gross, Benedict H. |
| Publisher | Harvard University |
| Source Sets | Harvard University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Rights | open |
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