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We study the possible dimension vectors of indecomposable parabolic bundles on the projective line, and use our answer to solve the problem of characterizing those collections of conjugacy classes of n×n matrices for which one can find matrices in their closures whose product is equal to the identity matrix. Both answers depend on the root system of a Kac-Moody Lie algebra. Our proofs use Ringel’s theory of tubular algebras, work of Mihai on the existence of logarithmic connections, the Riemann-Hilbert...

Indecomposable representations of the q-Deformed Virasoro algebra.

Ke-Qin Liu (1994)

Mathematische Zeitschrift

Index of Lie algebras of seaweed type.

Dergachev, Vladimir, Kirillov, Alexandre (2000)

Journal of Lie Theory

Indice du normalisateur du centralisateur d’un élément nilpotent dans une algèbre de Lie semi-simple

Anne Moreau (2006)

Bulletin de la Société Mathématique de France

L’indice d’une algèbre de Lie algébrique complexe est la codimension minimale de ses orbites coadjointes. Si $𝔤$ est semi-simple, son indice, $ind 𝔤$ , est égal à son rang, $rg 𝔤$ . Le but de cet article est d’établir une formule générale pour l’indice de $𝔫 (𝔤^{e})$ pour $e$ nilpotent, où $𝔫 (𝔤^{e})$ est le normalisateur dans $𝔤$ du centralisateur $𝔤^{e}$ de $e$ . Plus précisément, on obtient le résultat suivant, conjecturé par D. Panyushev : $ind 𝔫 (𝔤^{e}) = rg 𝔤 - dim 𝔷 (𝔤^{e}),$ où $𝔷 (𝔤^{e})$ est le centre de $𝔤^{e}$ . Panyushev obtient l’inégalité $ind 𝔫 (𝔤^{e}) \geq rg 𝔤 - dim 𝔷 (𝔤^{e})$ dans Panyushev 2003 et on montre que la maximalité...

Indice et polynômes invariants pour certaines algèbres de Lie.

Mustapha Rais, Patrice Tauvel (1992)

Journal für die reine und angewandte Mathematik

Induced modules for affine Lie algebras.

Futorny, Vyacheslav, Kashuba, Iryna (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Induction, deformation, and specialization of Lie algebra representations.

E.M. Friedlander, B.J. Parshall (1991)

Mathematische Annalen

Infinite dimensional Lie algebras: representations and applications

Goddard, P. (1985)

Proceedings of the Winter School "Geometry and Physics"

Infinite Grassmannians and moduli spaces of G-bundles.

M.S. Narasimhan, Shrawan Kumar (1994)

Mathematische Annalen

Infinite Root Systems, Representations of Graphs and Invariant Theory.

V.G. Kac (1980)

Inventiones mathematicae

Infinite-dimensional hyperkähler manifolds associated with Hermitian-symmetric affine coadjoint orbits

Alice Barbara Tumpach (2009)

Annales de l’institut Fourier

In this paper, we construct a hyperkähler structure on the complexification $𝒪^{ℂ}$ of any Hermitian symmetric affine coadjoint orbit $𝒪$ of a semi-simple $L^{*}$ -group of compact type, which is compatible with the complex symplectic form of Kirillov-Kostant-Souriau and restricts to the Kähler structure of $𝒪$ . By a relevant identification of the complex orbit $𝒪^{ℂ}$ with the cotangent space $T 𝒪$ of $𝒪$ induced by Mostow’s decomposition theorem, this leads to the existence of a hyperkähler structure on $T 𝒪$ compatible with...

Infinite-dimensional Lie groups and algebras in mathematical physics.

Schmid, Rudolf (2010)

Advances in Mathematical Physics

Infinitely many two-variable generalisations of the Alexander-Conway polynomial.

De Wit, David, Ishii, Atsushi, Links, Jon (2005)

Algebraic & Geometric Topology

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