3 research outputs found
Descriptions of strongly multiplicity free representations for simple Lie algebras
Let be a simple Lie algebra over the complex numbers
. Let be the center of the universal enveloping
algebra . Denote by the finite-dimensional simple
-module with highest weight . Lehrer and Zhang defined
the notion of strongly multiplicity free representations for simple Lie
algebras motivited by studying the structure of the endomorphism algebras in terms of the quotients of Kohno's
infinitesimal braid algebra. Kostant introduced the -invariant
endomorphism algebras and In this paper, we give some other
criterion for a multiplicity free representation to be a strongly multiplicity
free representation for simple Lie algebras by classifing the pairs
, which are multiplicity free irreducible modules
and for such pairs, and are generated by
generalizations of the quadratic Casimimir elements of