Multiplicity formulas for fundamental strings of representations of classical Lie algebras

Abstract

A new algorithm for computing branching rules and Clebsch-Gordan coefficients of unitary representations of compact groups

The spectrum on p-forms of a lens space

“…The main tool will be a closed explicit expression for m π k,p (µ) obtained in [LR17] (see Lemma 3.2 below). The expression for µ = n j=1 a j ε j ∈ P (G) depends only on…”

“…As a consequence, for any p 0 ≥ 0, we obtain a geometric characterization of lens spaces p-isospectral for all 0 ≤ p ≤ p 0 (Corollary 2.3). The main tool is a closed explicit formula from [LR17] for the multiplicity of weights in the irreducible representations of SO(2n) occurring in the decomposition of Sym k (C 2n ) ⊗ p (C 2n ) for any k ≥ 0 and 0 ≤ p ≤ n − 1.…”

“…As a consequence, for any p 0 ≥ 0, we obtain a geometric characterization of lens spaces p-isospectral for all 0 ≤ p ≤ p 0 (Corollary 2.3). The main tool is a closed explicit formula from [LR17] for the multiplicity of weights in the irreducible representations of SO(2n) occurring in the decomposition of Sym k (C 2n ) ⊗ p (C 2n ) for any k ≥ 0 and 0 ≤ p ≤ n − 1. Some results of this article have been recently used in [La17] to prove the non-existence of p-isospectral lens spaces (and lens orbifolds) for p in certain subsets of {0, 1, .…”

Generating functions for characters and weight multiplicities of irreducible 𝓈𝓁(4)-modules

“…and the numerators are given in the Appendix. Explicit formulas for the weight multiplicities of the representations of simple Lie algebras are in general difficult to obtain and are known only in particular cases, see for instance the recent paper [14], devoted to study this subject for the so-called fundamental string representations of the classical algebras. Regarding this point, we should mention that a possible application of the generating function…”

Weight multiplicity formulas for bivariate representations of classical Lie algebras

“…This article concerns on giving weight multiplicity formulas, continuing the previous authors' article [LR17]. In that article, it was determined, for a classical complex Lie algebra g, a closed explicit formula for the weight multiplicities of any representation of any p-fundamental string.…”