2010/01/07 by Yucai Su, Su, Yucai, R. B. Zhang +1 · 2 citations
Mathematics · Physics and Astronomy · #17B10 #17B20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math-ph #math.MP #math.QA #math.RT #msc:17B10 #msc:17B20
paper · pdf · doi:10.48550/arxiv.1001.1033
This is the final version to appear in the Journal of European Math Society. LaTeX, 31 pages
arxiv created 2010/10/15 · arxiv updated 2010/10/18
A Jantzen type filtration for generalised Varma 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.