Displaying similar documents to “The bar automorphism in quantum groups and geometry of quiver representations”

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...

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...

Singular components of Springer fibers in the two-column case

Lucas Fresse (2009)

Annales de l’institut Fourier

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We consider the Springer fiber ℬ u corresponding to a nilpotent endomorphism u of nilpotent order 2 . As a first result, we give a description of the elements of a given component of ℬ u which are fixed by the action of the standard torus relative to some Jordan basis of u . By using this result, we establish a necessary and sufficient condition of singularity for the components of ℬ u .

Rational points and Coxeter group actions on the cohomology of toric varieties

Gustav I. Lehrer (2008)

Annales de l’institut Fourier

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We derive a simple formula for the action of a finite crystallographic Coxeter group on the cohomology of its associated complex toric variety, using the method of counting rational points over finite fields, and the Hodge structure of the cohomology. Various applications are given, including the determination of the graded multiplicity of the reflection representation.