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On Newforms for Split Special Odd Orthogonal Groups
The theory of local newforms has been studied for the group of and recently and some other groups of small ranks. In this dissertation, we develop a newform theory for generic supercuspidal representations of over non-Archimedean local fields with odd characteristic by defining a family of open compact subgroup , (up to conjugacy) which are analogous to the groups in the classical theory of modular forms. We give lower bounds on the dimension of the fixed subspaces of 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].Mathematic