qs-analogue of weight multiplicity

1994 ◽  
pp. 44-47
Author(s):  
Nanhua Xi
Keyword(s):  
Weight Multiplicity

scholarly journals Weight multiplicity formulas for bivariate representations of classical Lie algebras

2018 ◽  
Vol 59 (8) ◽  
pp. 081705 ◽  
Author(s):  
Emilio A. Lauret ◽  
Fiorela Rossi Bertone
Keyword(s):  
Lie Algebras ◽  
Weight Multiplicity

Weight multiplicity for unitary groups

1984 ◽  
Vol 35 ◽  
pp. C-478
Author(s):  
V. Amar ◽  
U. Dozzio ◽  
C. Oleari
Keyword(s):  
Unitary Groups ◽  
Weight Multiplicity

scholarly journals When is the $q$-Multiplicity of a Weight a Power of $q$?

10.37236/8758 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Pamela E. Harris ◽  
Margaret Rahmoeller ◽  
Lisa Schneider ◽  
Anthony Simpson
Keyword(s):  
Lie Algebras ◽  
Dynkin Diagram ◽  
Fibonacci Numbers ◽  
Simple Lie Algebras ◽  
Weight Multiplicity ◽  
Highest Weight ◽  
Multiplicity Formula ◽  
Exhaustive List

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 $q$.

scholarly journals A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra

2021 ◽  
Vol 32 (1) ◽  
pp. 9-32
Author(s):  
C. Choi ◽  
◽  
S. Kim ◽  
H. Seo ◽  
◽  
...  
Keyword(s):  
Lie Algebra ◽  
Irreducible Representations ◽  
General Linear ◽  
Laurent Polynomials ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
Weight Multiplicity ◽  
Direct Sum ◽  
Direct Sum Decomposition ◽  
Multiplicity Free

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).

On the caluculation of weight multiplicity

1971 ◽  
Vol 8 (2) ◽  
pp. 810-812
Author(s):  
V. F. Molchanov
Keyword(s):  
Weight Multiplicity
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