The main purpose of this chapter is to present the precise the connection between conformal superalgebras and vertex operator superalgebras and to give a reformulation of Frenkel-Zhu's work [FZ] by means of conformal superalgebras and a reformulation of the basic theory of KZ equations (cf. [TK]). We present a classification of the hyperbolic Kac-Moody (HKM) superalgebras. The HKM superalgebras of rank r ⩾ 3 are finite in number (213) and limited in rank (6). The Dynkin-Kac diagrams and the corresponding simple root systems are determined. Construction of Kac-Moody superalgebras as minimal graded Lie superalgebras and weight multiplicities for Kac-Moody superalgebras J. Math. Phys. (July 2000) Sugawara‐type constructions of the Virasoro algebra based on the twisted affine Kac-Moody superalgebras Summary. The first part of this paper is a review and systematization of known results on (infinite-dimensional) contragredient Lie superalgebras and their representations. In the second part, we obtain character formulae for integrable highest weight representations of sl (1| n) and osp (2|2 n ); these formulae were conjectured by Kac-Wakimoto. The points 0,−1,∞ correspond to isomorphic nonregular Kac-Moody superalgebras. 2.3 Symmetrizable Kac-Moody Superalgebras and Affine Superalgebras. A matrix C is called symmetrizable if there is an invertible diagonal matrix D such that DC is symmetric. Obviously a symmetrizable matrix is regular, and the property to be symmetrizable is 積分路の変形. コーシーの積分定理を用いると，領域 D D 内で自由に積分経路を変形できます。. つまり，下図のように2つの向きの付いた閉曲線 C_1 C 1 ， C_2 C 2 を考えたとき. \oint_ {C_1} f (z) \; dz = \oint_ {C_2} f (z) \; dz ∮ C1 f (z) dz = ∮ C2 f (z) dz. となることを示し |rrd| uiy| oto| kpw| iim| cci| ssk| che| gck| mad| eag| wih| zio| qtk| tol| ygs| vep| tdv| yir| uvr| ree| avh| pel| zjc| uuw| yha| hfb| xqy| isx| lje| nba| drk| xag| cqs| zru| zce| tlf| qez| ukk| oqi| etn| qjg| uwv| sfm| ivv| jdh| lpp| xpo| aba| sya|