Generalised Jantzen filtration of Lie superalgebras I

Su, Yucai, and Zhang, R. B.. "Generalised Jantzen filtration of Lie superalgebras I." Journal of the European Mathematical Society 014.4 (2012): 1103-1133. <http://eudml.org/doc/277462>.

@article{Su2012,
abstract = {A Jantzen type filtration for generalised Verma modules of Lie superalgebras is introduced. In the case of type I Lie superalgebras, it is shown that the generalised Jantzen filtration for any Kac module is the unique Loewy filtration, and the decomposition numbers of the layers of the filtration are determined by the coefficients of inverse Kazhdan–Lusztig polynomials. Furthermore, the length of the Jantzen filtration for any Kac module is determined explicitly in terms of the degree of atypicality of the highest weight. These results are applied to obtain a detailed description of the submodule lattices of Kac modules.},
author = {Su, Yucai, Zhang, R. B.},
journal = {Journal of the European Mathematical Society},
keywords = {Lie superalgebras; Jantzen filtrations; Verma modules; Kazhdan–Lusztig polynomials; Lie superalgebras; Jantzen filtrations; Verma modules; Kazhdan-Lusztig polynomials},
language = {eng},
number = {4},
pages = {1103-1133},
publisher = {European Mathematical Society Publishing House},
title = {Generalised Jantzen filtration of Lie superalgebras I},
url = {http://eudml.org/doc/277462},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Su, Yucai
AU - Zhang, R. B.
TI - Generalised Jantzen filtration of Lie superalgebras I
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 4
SP - 1103
EP - 1133
AB - A Jantzen type filtration for generalised Verma modules of Lie superalgebras is introduced. In the case of type I Lie superalgebras, it is shown that the generalised Jantzen filtration for any Kac module is the unique Loewy filtration, and the decomposition numbers of the layers of the filtration are determined by the coefficients of inverse Kazhdan–Lusztig polynomials. Furthermore, the length of the Jantzen filtration for any Kac module is determined explicitly in terms of the degree of atypicality of the highest weight. These results are applied to obtain a detailed description of the submodule lattices of Kac modules.
LA - eng
KW - Lie superalgebras; Jantzen filtrations; Verma modules; Kazhdan–Lusztig polynomials; Lie superalgebras; Jantzen filtrations; Verma modules; Kazhdan-Lusztig polynomials
UR - http://eudml.org/doc/277462
ER -