Weight multiplicity formulas for bivariate representations of classical Lie algebras

Bertone, Fiorela Rossi

doi:10.1063/1.5043305

Cited by 1 publication

(2 citation statements)

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“…Problem 5.12. For some τ ∈ K different from every τ p , use [LR18] to give an expression for the spectral generating function associated to ∆ τ,Γ , for any Γ ⊂ T . Apply such expression to give a geometric characterization of τ -isospectral lens spaces.…”

Section: ] and [Lmr16b Tables 1-3])mentioning

confidence: 99%

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Recent results on the spectra of lens spaces

Miatello

Rossetti

2019

São Paulo J. Math. Sci.

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In this paper we report on recent results by several authors, on the spectral theory of lens spaces and orbifolds and similar locally symmetric spaces of rank one. Most of these results are related to those obtained by the authors in [IMRN (2016), 1054-1089], where the spectra of lens spaces were described in terms of the one-norm spectrum of a naturally associated congruence lattice. As a consequence, the first examples of Riemannian manifolds isospectral on p-forms for all p but not strongly isospectral were constructed.We also give a new elementary proof in the case of the spectrum on functions. In this proof, representation theory of compact Lie groups is avoided and replaced by the use of Molien's formula and a manipulation of the one-norm generating function associated to a congruence lattice. In the last four sections we present several recent results, open problems and conjectures on the subject.

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Section: ] and [Lmr16b Tables 1-3])mentioning

confidence: 99%

“…As a continuation of [LR17], in [LR18] expressions were given for the weight multiplicities of the irreducible representations of G = SO(2n) having highest weight kε 1 + lε 2 for all k ≥ l ≥ 0. These representations are called bivariate representations because their highest weights are integral combinations of the first two fundamental weights.…”

Section: 3mentioning

confidence: 99%