weight multiplicity
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2021 ◽  
Vol 32 (1) ◽  
pp. 9-32
Author(s):  
C. Choi ◽  
◽  
S. Kim ◽  
H. Seo ◽  
◽  
...  

We first present a filtration on the ring Ln of Laurent polynomials such that the direct sum decomposition of its associated graded ring grLn agrees with the direct sum decomposition of grLn, as a module over the complex general linear Lie algebra gl(n), into its simple submodules. Next, generalizing the simple modules occurring in the associated graded ring grLn, we give some explicit constructions of weight multiplicity-free irreducible representations of gl(n).



2020 ◽  
Vol 11 (1) ◽  
pp. 141-167 ◽  
Author(s):  
Kevin Chang ◽  
Pamela E. Harris ◽  
Erik Insko


10.37236/8758 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Pamela E. Harris ◽  
Margaret Rahmoeller ◽  
Lisa Schneider ◽  
Anthony Simpson

Berenshtein and Zelevinskii provided an exhaustive list of pairs of weights $(\lambda,\mu)$ of simple Lie algebras $\mathfrak{g}$ (up to Dynkin diagram isomorphism) for which the multiplicity of the weight $\mu$ in the representation of $\mathfrak{g}$ with highest weight $\lambda$ is equal to one. Using Kostant's weight multiplicity formula we describe and enumerate the contributing terms to the multiplicity for subsets of these pairs of weights and show that, in these cases, the cardinality of these contributing sets is enumerated by (multiples of) Fibonacci numbers. We conclude by using these results to compute the associated $q$-multiplicity for the pairs of weights considered, and conjecture that in all cases the $q$-multiplicity of such pairs of weights is given by a power of $q$.



2018 ◽  
Vol 59 (8) ◽  
pp. 081705 ◽  
Author(s):  
Emilio A. Lauret ◽  
Fiorela Rossi Bertone










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