Representations and invariant equations for the exotic conformal Galilei algebra

publisher[Abstract] We investigate the reducibility of highest weight Verma modules over the exotic conformal Galilei algebra. This is done by explicitly constructing all singular vectors, and then deducing irreducibility of the associated quotient modules. A resulting classification of infinite dimensional irreducible modules is presented. By making use of the singular vectors, we also present a system of differential equations invariant under the exotic conformal Galilei group. [概要] エキゾチック共形Galilei代数の最高ウエイト表現について研究し, 既約なVerma加群の分類を得た。分類に用いたのは, Verma加群, および付随する商加群の特異ベクトルをすべて求めるという方法である。また, これらの特異ベクトルを用いて, エキゾチック共形ガリレイ群の作用で不変な偏微分方程式系を導いた