Singular components of Springer fibers in the two-column case

Lucas Fresse

Displaying similar documents to “Singular components of Springer fibers in the two-column case”

Surprising properties of centralisers in classical Lie algebras

Oksana Yakimova (2009)

Annales de l’institut Fourier

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Let $𝔤$ be a classical Lie algebra, , either ${𝔤𝔩}_{n}$ , ${𝔰𝔭}_{n}$ , or ${𝔰𝔬}_{n}$ and let $e$ be a nilpotent element of $𝔤$ . We study various properties of the centralisers $𝔤_{e}$ . The first four sections deal with rather elementary questions, like the centre of $𝔤_{e}$ , commuting varieties associated with $𝔤_{e}$ , or centralisers of commuting pairs. The second half of the paper addresses problems related to different Poisson structures on $𝔤_{e}^{*}$ and symmetric invariants of $𝔤_{e}$ .

Quadratic Differentials and Equivariant Deformation Theory of Curves

Bernhard Köck, Aristides Kontogeorgis (2012)

Annales de l’institut Fourier

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Given a finite $p$ -group $G$ acting on a smooth projective curve $X$ over an algebraically closed field $k$ of characteristic $p$ , the dimension of the tangent space of the associated equivariant deformation functor is equal to the dimension of the space of coinvariants of $G$ acting on the space $V$ of global holomorphic quadratic differentials on $X$ . We apply known results about the Galois module structure of Riemann-Roch spaces to compute this dimension when $G$ is cyclic or when the action of $G$ on...

Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Cédric Bonnafé, Christophe Hohlweg (2006)

Annales de l’institut Fourier

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We construct a subalgebra $Σ^{'} (W_{n})$ of dimension $2 \cdot 3^{n - 1}$ of the group algebra of the Weyl group $W_{n}$ of type $B_{n}$ containing its usual Solomon algebra and the one of $𝔖_{n}$ : $Σ^{'} (W_{n})$ is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras $Σ^{'} (W_{n}) \to Z Irr (W_{n})$ . Jöllenbeck’s construction of irreducible characters of the symmetric group by using the coplactic equivalence classes can then be transposed to $W_{n}$ . In an appendix, P. Baumann and C. Hohlweg present in an...

The combinatorics of quiver representations

Harm Derksen, Jerzy Weyman (2011)

Annales de l’institut Fourier

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We give a description of faces, of all codimensions, for the cones spanned by the set of weights associated to the rings of semi-invariants of quivers. For a triple flag quiver and its faces of codimension 1 this description reduces to the result of Knutson-Tao-Woodward on the facets of the Klyachko cone. We give new applications to Littlewood-Richardson coefficients, including a product formula for LR-coefficients corresponding to triples of partitions lying on a wall of the Klyachko...

An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity

H.-Ch. Graf von Bothmer, Wolfgang Ebeling, Xavier Gómez-Mont (2008)

Annales de l’institut Fourier

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Let $(V, 0)$ be a germ of a complete intersection variety in $ℂ^{n + k}$ , $n > 0$ , having an isolated singularity at $0$ and $X$ be the germ of a holomorphic vector field having an isolated zero at $0$ and tangent to $V$ . We show that in this case the homological index and the GSV-index coincide. In the case when the zero of $X$ is also isolated in the ambient space $ℂ^{n + k}$ we give a formula for the homological index in terms of local linear algebra.