Representation theory of affine superalgebras at the critical level (Q1126765)

The author discusses im some special cases significant problems in character formulas and representations of affine Lie superalgebras. In point 1: Characters of affine superalgebras, the author claims a special formula for the denominator identity of \(\widehat{A} (1,1)\), obtained by analysing the super boson-fermion correspondence. A more complicated formula is stated in case \(\widehat{A} (2,2)\). Moreover a character formula is given in an atypical case for \(\widehat{sl} (2,1)\) at the critical level. In point 2: Free field construction of atypical \(\widehat{sl} (2,1)\)-modules at the critical level, the author gives an explicit construction of atypical highest weight modules at the critical level for \(\widehat{sl} (2,1)\). In point 3: Mock theta identities and the associated modular functions, the mock theta function associated to \(\widehat{B} (1,1)\) is given and its modular transformation is dedicated.