2022-08-09T02:28:47Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000040152021-03-01T19:47:34ZSU(2; 2) の主系列の(g;K)-加群構造と関連するWHITTAKER 関数THE (g;K)-MODULE STRUCTURE OF PRINCIPAL SERIES AND RELATED WHITTAKER FUNCTIONS OF SU(2; 2)BAYARMAGNAI, GOMBODORJ9279410University of Tokyo (東京大学)博士(数理科学)This is an overview of my thesis which consists of two papers. Our principal research interest lies in the theory of automorphic forms of many variables, especially in the spherical functions over real semisimple Lie groups, and their applications to the theory of automorphic forms. Though this is a natural and fundamental problem, precise studies for the case of higher-rank Lie groups are very recent. Over the recent decades representation theory gained a central role in modern mathematics, linking such areas as number theory, differential equations, algebraic and arithmetic geometry and theory of automorphic forms. In particular, the Whittaker models are one of the main ingredients of the theory in Fourier expansions of automorphic form at cusps. In this sense, explicit knowledge of Whittaker functions is very important for deeper studies of automorphic forms. My research in doctoral course focuses on various Whittaker models of the principal series representations of SU(2, 2) obtained by parabolic induction. The main object of this paper is the space of algebraic Whittaker vectors attached to the principaL series representations of SU(2,2), parabolically induced with respect to the minimal parabolic subgroup Pmin. In this setting, firstly, we describe completely the whole structure of the (g, K)-modules of these representations in the first part of thepapers, entitled'"The (g, K)-module structures of principal series ofSU(2, 2)". Secondly, we obtain various integral expressions of some smooth Whittaker functions with certain K-types to provide an explicit-form of generators of the space of algebraic Whittaker vectors locally in the paper entitled "Explicit evaluation of certain Jacquet integrals on SU(2, 2)".thesis2009-03-232009-03-23application/pdfapplication/pdf甲第24980号https://repository.dl.itc.u-tokyo.ac.jp/record/4015/files/BayarmagnaiG_21_3_PhD_a.pdfhttps://repository.dl.itc.u-tokyo.ac.jp/record/4015/files/BayarmagnaiG_21_3_PhD_b.pdfeng