Characters and composition factor multiplicities for the Lie superalgebra gl(m/n) release_kz3k36qs6vbalj5rqsxtm53sxa

by J. Van der Jeugt, R.B. Zhang

Released as a report .

1998  

Abstract

The multiplicities a_lambda,mu of simple modules L(mu) in the composition series of Kac modules V(lambda) for the Lie superalgebra gl(m/n) were described by Serganova, leading to her solution of the character problem for gl(m/n). In Serganova's algorithm all mu with nonzero a_lambda,mu are determined for a given lambda; this algorithm turns out to be rather complicated. In this Letter a simple rule is conjectured to find all nonzero a_lambda,mu for any given weight mu. In particular, we claim that for an r-fold atypical weight mu there are 2^r distinct weights lambda such that a_lambda,mu=1, and a_lambda,mu=0 for all other weights lambda. Some related properties on the multiplicities a_lambda,mu are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan-Lusztig polynomials is discussed.
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Type  report
Stage   submitted
Date   1998-11-04
Version   v1
Language   en ?
Number  TWI-98-J
arXiv  math/9811015v1
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