Эта публикация цитируется в
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Representations of affine superalgebras and mock theta functions. III
V. G. Kaca,
M. Wakimotob a Department of Mathematics, Massachusetts Institute of Technology
b 12-4 Karato-Rokkoudai, Kita-ku, Kobe 651-1334, Japan
Аннотация:
We study modular invariance of normalized supercharacters of tame
integrable modules over an affine Lie superalgebra, associated to an
arbitrary basic Lie superalgebra
$\mathfrak g$. For this we develop a several
step modification process of multivariable mock theta functions,
where at each step a Zwegers' type ‘modifier’ is used. We show that the
span of the resulting modified normalized supercharacters is
$\operatorname{SL}_2(\mathbb Z)$-invariant, with the transformation matrix
equal, in the case the Killing form
on
$\mathfrak g$ is non-degenerate, to that for the basic
defect 0 subalgebra
$\mathfrak g^!$ of
$\mathfrak g$, orthogonal to a maximal
isotropic set of roots of
$\mathfrak g$.
Ключевые слова:
basic finite-dimensional Lie superalgebra, affine Lie superalgebra,
tame integrable modules, normalized supercharacters, mock theta function,
modification process, modular invariance.
УДК:
512.554
MSC: 17B67,
33E05 Поступило в редакцию: 06.05.2015
Исправленный вариант: 21.10.2015
Язык публикации: английский
DOI:
10.4213/im8408