The existence of equivariant pure free resolutions

David Eisenbud; Gunnar Fløystad; Jerzy Weyman

Displaying similar documents to “The existence of equivariant pure free resolutions”

Transgression and Clifford algebras

Rudolf Philippe Rohr (2009)

Annales de l’institut Fourier

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Let $W$ be a differential (not necessarily commutative) algebra which carries a free action of a polynomial algebra $S P$ with homogeneous generators $p_{1}, \dots, p_{r}$ . We show that for $W$ acyclic, the cohomology of the quotient $H (W /$ $< p_{1}, \dots, p_{r} >)$ is isomorphic to a Clifford algebra $Cl (P, B)$ , where the (possibly degenerate) bilinear form $B$ depends on $W$ . This observation is an analogue of an old result of Borel in a non-commutative context. As an application, we study the case of $W$ given by the quantized Weil algebra...

The Grothendieck group of GL(F)×GL(G)-equivariant modules over the coordinate ring of determinantal varieties

J. Weyman (1998)

Colloquium Mathematicae

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The PBW filtration, Demazure modules and toroidal current algebras.

Feigin, Evgeny (2008)

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

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Hasse–Schmidt derivations, divided powers and differential smoothness

Luis Narváez Macarro (2009)

Annales de l’institut Fourier

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Let $k$ be a commutative ring, $A$ a commutative $k$ -algebra and $D$ the filtered ring of $k$ -linear differential operators of $A$ . We prove that: (1) The graded ring $gr D$ admits a canonical embedding $θ$ into the graded dual of the symmetric algebra of the module $Ω_{A / k}$ of differentials of $A$ over $k$ , which has a canonical divided power structure. (2) There is a canonical morphism $ϑ$ from the divided power algebra of the module of $k$ -linear Hasse–Schmidt integrable derivations of $A$ to $gr D$ . (3) Morphisms $θ$ and...

Smooth components of Springer fibers

William Graham, R. Zierau (2011)

Annales de l’institut Fourier

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This article studies components of Springer fibers for $𝔤𝔩 (n)$ that are associated to closed orbits of $G L (p) \times G L (q)$ on the flag variety of $G L (n), n = p + q$ . These components occur in any Springer fiber. In contrast to the case of arbitrary components, these components are smooth varieties. Using results of Barchini and Zierau we show these components are iterated bundles and are stable under the action of a maximal torus of $G L (n)$ . We prove that if $ℒ$ is a line bundle on the flag variety associated to a dominant weight,...

On bounded generalized Harish-Chandra modules

Ivan Penkov, Vera Serganova (2012)

Annales de l’institut Fourier

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Let $𝔤$ be a complex reductive Lie algebra and $𝔨 \subset 𝔤$ be any reductive in $𝔤$ subalgebra. We call a $(𝔤, 𝔨)$ -module $M$ bounded if the $𝔨$ -multiplicities of $M$ are uniformly bounded. In this paper we initiate a general study of simple bounded $(𝔤, 𝔨)$ -modules. We prove a strong necessary condition for a subalgebra $𝔨$ to be bounded (Corollary 4.6), to admit an infinite-dimensional simple bounded $(𝔤, 𝔨)$ -module, and then establish a sufficient condition for a subalgebra $𝔨$ to be bounded (Theorem 5.1). As a result we are...