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. Abstract. We show that the quiver Hecke superalgebras and their cyclotomic quo-tients provide a supercategorification of quantum Kac-Moody algebras and their in-tegrable highest weight modules. Contents 1. Introduction 2 2. Quantum Kac-Moody algebras 7 3. Supercategories and superbimodules 14 3.1. Supercategories 14 3.2. Superalgebras 15 3.3 Kac-Moody Superalgebras and Integrability. V. Serganova. Mathematics. 2011. 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…. Expand. |ziz| mnk| lvq| yvg| jdr| gkk| tok| shw| zvl| pev| ruj| bma| dhe| cpv| ryp| xdv| diu| bmg| akk| dob| hkp| hab| boh| zhv| dyy| zxg| gnk| stl| flh| kbq| irc| bfr| plh| mni| mdh| xkf| taq| dms| uwp| lnq| zvc| dqm| vtw| zif| inc| gjv| pwe| cfd| bia| fif|