http://hdl.handle.net/1721.1/7845 Tue, 21 May 2013 20:37:56 GMT 2013-05-21T20:37:56Z http://hdl.handle.net/1721.1/65037 Equivalent statements to exotic p.1. structures on the 4-sphere. Gerra, Ralph Alexander Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1973.; Vita.; Bibliography: leaves 20-21. Mon, 01 Jan 1973 05:00:00 GMT http://hdl.handle.net/1721.1/65037 1973-01-01T05:00:00Z http://hdl.handle.net/1721.1/54665 Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula Tabony, Sawyer In their paper Metaplectic Forms, D. A. Kazhdan and S. J. Patterson developed a generalization of automorphic forms that are defined on metaplectic groups. These groups are non-trivial covering groups of usual algebraic groups, and the forms defined on them are representations that respect the covering. As in the case for automorphic forms, these representations fall into a principle series, indexed by characters on a torus of the metaplectic group, and there is an associated an L-function. In the final section of their paper, an equivalence is shown in the rank one case between this -function and an Dirichlet series defined using Gauss sums, in order to demonstrate the arithmetic content. In this paper we reexamine this connection in the particular case that was discussed in Metaplectic Forms. By looking through the scope of twisted multiplicativity, a property of L-series, the computation is simplified and more easily generalized. Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.; Cataloged from PDF version of thesis.; Includes bibliographical references (p. 29). Thu, 01 Jan 2009 05:00:00 GMT http://hdl.handle.net/1721.1/54665 2009-01-01T05:00:00Z http://hdl.handle.net/1721.1/54664 Rings of regular functions on spherical nilpotent orbits for complex classical groups Suk, Tonghoon Let G be a classical group and let g be its Lie algebra. For a nilpotent element X E g, the ring R(Ox) of regular functions on the nilpotent orbit Ox is a G-module. In this thesis, we will decompose it into irreducible representations of G for some spherical nilpotent orbits. Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.; Cataloged from PDF version of thesis.; Includes bibliographical references (p. 16). Thu, 01 Jan 2009 05:00:00 GMT http://hdl.handle.net/1721.1/54664 2009-01-01T05:00:00Z http://hdl.handle.net/1721.1/47899 Differential posets and dual graded graphs Qing, Yulan, S.M. Massachusetts Institute of Technology In this thesis I study r-differential posets and dual graded graphs. Differential posets are partially ordered sets whose elements form the basis of a vector space that satisfies DU-UD=rI, where U and D are certain order-raising and order-lowering operators. New results are presented related to the growth and classification of differential posets. In particular, we prove that the rank sequence of an r-differential poset is bounded above by the Fibonacci sequence and that there is a unique poset with such a maximum rank sequence. We also prove that a 1-differential lattice is either Young's lattice or the Fibonacci lattice. In the second part of the thesis, we present a series of new examples of dual graded graphs that are not isomorphic to the ones presented in Fomin's original paper. Thesis (S. M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.; Includes bibliographical references (leaf 53). Tue, 01 Jan 2008 05:00:00 GMT http://hdl.handle.net/1721.1/47899 2008-01-01T05:00:00Z