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ABSTRACT
A monomial basis and a filtration of subalgebras for the universal enveloping algebra 𝔘(𝔤 l ) of a complex simple Lie algebra 𝔤 l of type A l is given in this note. In particular, a new multiplicity formula for the Weyl module V(λ) of 𝔘(𝔤 l ) is obtained in this note.
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ACKNOWLEDGMENT
This work was supported in part by the NNSFC (10271088) and RFDP of Higher Education (20040247024). The first author is also grateful to the Abdus Salam International Centre for Theoretical Physics for its financial support and hospitability during his visit.
Communicated by B. Parshall.