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Unitarily invariant geometry on Grassmann manifold /Shen, Hongrui. January 2006 (has links)
Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 57-59). Also available in electronic version.
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Geometric pullback formula for unitary Shimura varietiesDung, Nguyen Chi January 2022 (has links)
In this thesis we study Kudla’s special cycles of codimension 𝑟 on a unitary Shimura variety Sh(U(𝑚 − 1,1)) together with an embedding of a Shimura subvariety Sh(U(𝑚 − 1,1)). We prove that when 𝑟 = 𝑛 − 𝑚, for certain cuspidal automorphic representations 𝜋 of the quasi-split unitary group U(𝑟,𝑟) and certain cusp forms ⨍ ∈ 𝜋, the geometric volume of the pullbackof the arithmetic theta lift of ⨍ equals the special value of the standard 𝐿-function of 𝜋 at 𝑠 = (𝑚 − 𝑟 + 1)/2. As ingredients of the proof, we also give an exposition of Kudla’s geometric Siegel-Weil formula and Yuan-Zhang-Zhang’s pullback formula in the setting of unitary Shimura varieties, as well as Qin’s integral representation result for 𝐿-functions of quasi-split unitary groups.
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Endoscopic codes for unitary groups over the realsRubanovich, Dmitry, January 2009 (has links)
Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematical Sciences." Includes bibliographical references (p. 74).
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Lokale Verkettungsintegrale und ihre Nenner für die speziellen linearen und unitären Gruppen dreier VariablerEverling, Ulrich. January 1991 (has links)
Thesis (Doctoral)--Universität Bonn, 1991. / Includes bibliographical references.
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Multiplicity One Results and Explicit Formulas for Quasi-Split p-adic Unitary GroupsKhoury, Michael John, Jr. 11 September 2008 (has links)
No description available.
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Root subgroups of the rank two unitary groupsHenes, Matthew Thomas 01 January 2005 (has links)
Discusses certain one-parameter subgroups of the low-rank unitary groups called root subgroups. Unitary groups also have representations of Lie type which means they consist of transformations that act as automorphisms of an underlying Lie algebra, in this case the special linear algebra. Exploring this definition of the unitary groups, we find a correlation, via exponentiation, to the basis elements of Lie algebra.
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An alternative proof of genericity for unitary group of three variablesWang, Chongli January 2016 (has links)
In this thesis, we prove that local genericity implies globally genericity for the quasi-split unitary group U3 for a quadratic extension of number fields E/F. We follow [Fli1992] and [GJR2001] closely, using the relative trace formula approach. Our main result is the existence of smooth transfer for the relative trace formulae in [GJR2001], which is circumvented there. The basic idea is to compute the Mellin transform of Shalika germ functions and show that they are equal in the unitary case and the general linear case.
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An integral representation of automorphic L-function for quasi-split unitary groups /Qin, Yujun. January 2004 (has links)
Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 61-62). Also available in electronic version. Access restricted to campus users.
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Study of pion production from the two-nucleon system within a relativistic unitary modelSammarruca-Machleidt, Francesca January 1988 (has links)
In this work, we explore the NN → πNN reaction within a relativistic model, consistent with two- and three-body unitarity, for the NN and πNN coupled systems. The model is based on effective hadronic interactions. After describing the theoretical input, we compare the predicted NN phase parameters with the phase shift analysis. Our predictions for the NN → πNN spin observables are compared with the available data and with predictions from other models. A clear model dependence is observed. We also examine systematically the dependence of these spin observables on various components of the dynamical input. We identify and isolate some problems related to the present approach and we point out possible directions for future research. / Ph. D.
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A Kudla-Rapoport Formula for Exotic Smooth Models of Odd DimensionYao, Haodong January 2024 (has links)
In this thesis, we prove a Kudla-Rapoport conjecture for 𝓨-cycles on exotic smooth unitary Rapoport-Zink spaces of odd arithmetic dimension, i.e. the arithmetic intersection numbers for 𝓨-cycles equals the derivatives of local representation density.
We also compare 𝓩-cycles and 𝓨-cycles on these RZ spaces. The method is to relate both geometric and analytic sides to the even dimensional case and reduce the conjecture to the results in \cite{LL22}.
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